NCERT Exemplar solutions for Mathematics [English] Class 10 chapter 13 - Statistics and Probability [Latest edition]

In the formula `barx = a + (f_i d_i)/f_i`, for finding the mean of grouped data d_i’s are deviations from a of ______.

While computing mean of grouped data, we assume that the frequencies are ______.

If x_i’s are the midpoints of the class intervals of grouped data, f_i’s are the corresponding frequencies and `barx` is the mean, then `sum(f_ix_i - barx)` is equal to ______.

In the formula `barx = a + h((sumf_iu_i)/(sumf_i))`, for finding the mean of grouped frequency distribution, u_i = ______.

The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its ______.

For the following distribution:

The sum of lower limits of the median class and modal class is:

Consider the following frequency distribution:

The upper limit of the median class is:

For the following distribution:

The modal class is ______.

Consider the data:

The difference of the upper limit of the median class and the lower limit of the modal class is:

The times, in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below:

The number of athletes who completed the race in less than 14.6 seconds is:

Consider the following distribution:

The frequency of the class 30 – 40 is:

If an event cannot occur, then its probability is ______.

Which of the following cannot be the probability of an event?

An event is very unlikely to happen. Its probability is closest to ______.

If the probability of an event is p, the probability of its complementary event will be ______.

The probability expressed as a percentage of a particular occurrence can never be ______.

If P(A) denotes the probability of an event A, then ______.

A card is selected from a deck of 52 cards. The probability of its being a red face card is ______.

The probability that a non leap year selected at random will contain 53 sundays is ______.

When a die is thrown, the probability of getting an odd number less than 3 is ______.

A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is ______.

The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is ______.

A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6,000 tickets are sold, how many tickets has she bought?

One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is ______.

Someone is asked to take a number from 1 to 100. The probability that it is a prime is ______.

A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is ______.

The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement? Give reason.

In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula `barx = a + (sumf_i d_i)/(sumf_i)` where a is the assumed mean. a must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.

Is it true to say that the mean, mode and median of grouped data will always be different? Justify your answer

Will the median class and modal class of grouped data always be different? Justify your answer.

In a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is `1/4`. Is this correct? Justify your answer

A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3) (figure). Are the outcomes 1, 2 and 3 equally likely to occur? Give reasons.

Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36? Why?

When we toss a coin, there are two possible outcomes - Head or Tail. Therefore, the probability of each outcome is `1/2`. Justify your answer.

A student says that if you throw a die, it will show up 1 or not 1. Therefore, the probability of getting 1 and the probability of getting ‘not 1’ each is equal to `1/2`. Is this correct? Give reasons. 

I toss three coins together. The possible outcomes are no heads, 1 head, 2 heads and 3 heads. So, I say that probability of no heads is `1/4`. What is wrong with this conclusion?

If you toss a coin 6 times and it comes down heads on each occasion. Can you say that the probability of getting a head is 1? Give reasons.

Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be a tail? Give reasons.

If I toss a coin 3 times and get head each time, should I expect a tail to have a higher chance in the 4^th toss? Give reason in support of your answer.

A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since this situation has only two possible outcomes, so, the probability of each is `1/2`. Justify 

Find the mean of the distribution:

Calculate the mean of the scores of 20 students in a mathematics test:

Calculate the mean of the following data:

The following table gives the number of pages written by Sarika for completing her own book for 30 days:

Find the mean number of pages written per day.

The daily income of a sample of 50 employees are tabulated as follows:

Find the mean daily income of employees.

An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table:

The weights (in kg) of 50 wrestlers are recorded in the following table:

Find the mean weight of the wrestlers.

The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below:

Find the mean mileage. The manufacturer claimed that the mileage of the model was 16 km/litre. Do you agree with this claim?

The following is the distribution of weights (in kg) of 40 persons:

Construct a cumulative frequency distribution (of the less than type) table for the data above.

The following table shows the cumulative frequency distribution of marks of 800 students in an examination:

Construct a frequency distribution table for the data above.

Form the frequency distribution table from the following data:

Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class:

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:

Form: Less than type cumulative frequency distribution.

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:

Form: More than type cumulative frequency distribution.

Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class:

Form the frequency distribution table for the data.

Weekly income of 600 families is tabulated below:

Compute the median income.

The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows:

Calculate the median bowling speed.

The monthly income of 100 families are given as below:

Calculate the modal income.

The weight of coffee in 70 packets are shown in the following table:

Determine the modal weight.

Two dice are thrown at the same time. Find the probability of getting same number on both dice.

Two dice are thrown at the same time. Find the probability of getting different numbers on both dice.

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 7?

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is 1?

Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 6

Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 12

Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 7

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is less than 9.

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.

A coin is tossed two times. Find the probability of getting at most one head.

A coin is tossed 3 times. List the possible outcomes. Find the probability of getting all heads

A coin is tossed 3 times. List the possible outcomes. Find the probability of getting at least 2 heads

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.

A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random. Find the probability of this ball being a red ball.

A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random. Find the probability of this ball being a green ball.

A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random. Find the probability of this ball being a not a blue ball.

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a heart.

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a king.

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. What is the probability that the card is a club?

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. What is the probability that the card is 10 of hearts?

All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value 7

All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value greater than 7

All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value less than 7

An integer is chosen between 0 and 100. What is the probability that it is divisible by 7?

An integer is chosen between 0 and 100. What is the probability that it is not divisible by 7?

Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number

Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has a square number

A letter of English alphabets is chosen at random. Determine the probability that the letter is a consonant.

There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs 100 each, 100 of them contain a cash prize of Rs 50 each and 200 of them contain a cash prize of Rs 10 each and rest do not contain any cash prize. If they are well shuffled and an envelope is picked up out, what is the probability that it contains no cash prize?

Box A contains 25 slips of which 19 are marked Rs 1 and other are marked Rs 5 each. Box B contains 50 slips of which 45 are marked Rs 1 each and others are marked Rs 13 each. Slips of both boxes are poured into a third box and resuffled. A slip is drawn at random. What is the probability that it is marked other than Rs 1?

A carton of 24 bulbs contain 6 defective bulbs. One bulbs is drawn at random. What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?

A child’s game has 8 triangles of which 3 are blue and rest are red and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a triangle

A child’s game has 8 triangles of which 3 are blue and rest are red and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a square

A child’s game has 8 triangles of which 3 are blue and rest are red and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a square of blue colour

A child’s game has 8 triangles of which 3 are blue and rest are red and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a triangle of red colour

In a game, the entry fee is Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she loses the entry fee.

In a game, the entry fee is Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she gets double entry fee.

In a game, the entry fee is Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she just gets her entry fee.

A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded. How many different scores are possible?

A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded. What is the probability of getting a total of 7?

A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects and 3 have major defects. Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is acceptable to Varnika?

A lot consists of 48 mobile phones of which 42 are good, 3 have only minor defects and 3 have major defects. Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is acceptable to the trader?

A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is not red?

A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is white?

At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the first player wins a prize?

At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the second player wins a prize, if the first has won?