Balbharati solutions for Algebra (Mathematics 1) [English] 10 Standard SSC Maharashtra State Board chapter 5 - Probability [Latest edition]

How many possibilities is the following?
Vanita knows the following sites in Maharashtra. She is planning to visit one of them in her summer vacation.

Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli, Raigad, Matheran, Anandavan.

How many possibilities is following?

Any day of a week is to be selected randomly.

How many possibilities is following?

Select one card from the pack of 52 cards.

How many possibilities is following?

One number from 10 to 20 is written on each card. Select one card randomly.

For the following experiment write sample space ‘S’ and number of sample points n(S).

One coin and one die are thrown simultaneously.

For the following experiment write sample space ‘S’ and number of sample points n(S).

Two-digit numbers are formed using digits 2, 3 and 5 without repeating a digit.

The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop.

In the month of March 2019, Find the days on which the date is a multiple of 5. (see the given page of the calender)

Form a ‘Road safety commitee’ of two, from 2 boys (B₁, B₂) and 2 girls(G₁, G₂). Complete the following activity to write the sample space.
(a) Committee of 2 boys =

b) Committee of 2 girls =

(c) Committee of one boy and one girl =

Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).
One die is rolled,
Event  A : Even number on the upper face. 
Event  B : Odd number on the upper face.
Event  C : Prime number on the upper face.

Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).

Two dice are rolled simultaneously,
Event  A : The sum of the digits on upper faces is a multiple of 6. 
Event B : The sum of the digits on the upper faces is minimum 10.
Event  C : The same digit on both the upper faces.

Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).

Three coins are tossed simultaneously.
Condition for event A : To get at least two heads. 
Condition for event B : To get no head.
Condition for event C : To get head on the second coin.

Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).

Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits.
Condition for event A : The number formed is even
Condition for event B : The number formed is divisible by 3.
Condition for event C : The number formed is greater than 50.

Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).

From three men and two women, environment committee of two persons is to be formed.
Condition for event A : There must be at least one woman member.
Condition for event B : One man, one woman committee to be formed.
Condition for event C : There should not be a woman member.

Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).

One coin and one die are thrown simultaneously.
Condition for event A : To get head and an odd number.
Condition for event B : To get a head or tail and an even number. 
Condition for event C : Number on the upper face is greater than 7 and tail on the coin.

If two coins are tossed, find the probability of the following event.

Getting at least one head.

If two coins are tossed, find the probability of the following event.
Getting no head ?

If two dice are rolled simultaneously, find the probability of the following event.
The sum of the digits on the upper faces is at least 10.

If two dice are rolled simultaneously, find the probability of the following event. The sum of the digits on the upper faces is 33.

If two dice are rolled simultaneously, find the probability of the following event.
The digit on the first die is greater than the digit on second die.

There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn - shows an even number.

There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn - shows a number which is a multiple of 5.

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is an odd number?

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is a multiple of 5 ?

A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is – an ace.

A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is a spade.

Which number cannot represent a probability?

Choose the correct alternative answer for the following question.

A die is rolled. What is the probability that the number appearing on upper face is less than 3 ?

Choose the correct alternative answer for the following question.

 What is the probability of the event that a number chosen from 1 to 100 is a prime number ?

Choose the correct alternative answer for the following question.

There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5 ?

Choose the correct alternative answer for the following question.

If n(A) = 2, P(A) = `1/5`, then n(S) = ?

Basketball players John, Vasim, Akash were practising the ball drop in the basket. The probabilities of success for John, Vasim and Akash are `4/5`, 0.83 and 58% respectively. Who had the greatest probability of success? 

In a hockey team, there are 6 defenders, 4 offenders, and 1 goalee. Out of these, one player is to be selected randomly as a captain. Find the probability of the selection that – The goalee will be selected.

In a hockey team there are 6 defenders, 4 offenders and 1 goalee. Out of these, one player is to be selected randomly as a captain. Find the probability of the selection that – A defender will be selected.

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, a red balloon

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, a blue balloon

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets,a green balloon.

A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue?

Six faces of a die are as shown below.

If the die is rolled once, find the probability of - ‘A’ appears on upper face.

Six faces of a die are as shown below.

If the die is rolled once, find the probability of -‘D’ appears on upper face.

A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears an odd number .

A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears a complete square number.

Length and breadth of a rectangular garden are 77 m and 50 m. There is a circular lake in the garden having diameter 14 m. Due to wind, a towel from a terrace on a nearby building fell into the garden. Then find the probability of the event that it fell in the lake.

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at 8.

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at an odd number.

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at a number greater than 2.

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at  a number less than 9.

There are six cards in a box, each bearing a number from 0 to 5. Find the probability of the following event, that a card drawn show, a natural number.

There are six cards in a box, each bearing a number from 0 to 5. Find the probability of the following event, that a card drawn show,  number less than 1.

There are six cards in a box, each bearing a number from 0 to 5. Find the probability of the following event, that a card drawn show,  a whole number.

There are six cards in a box, each bearing a number from 0 to 5. Find the probability of the following event, that a card drawn show, a number is greater than 5.

A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is – red.

A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is –not red.

A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is – either red or white.

Each card bears one letter from the word ‘mathematics’ The cards are placed on a table upside down. Find the probability that a card drawn bears the letter ‘m’.

Out of 200 students from a school, 135 like Kabbaddi and the remaining students do not like the game. If one student is selected at random from all the students, find the probability that the student selected dosen't like Kabbaddi.

A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a - prime number.

A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a -  multiple of 4.

A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a - multiple of 11.

The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.

Do the following activity -
Activity I : Total number of students in your class, n(S) =

Number of students from your class, wearing spectacles, n(A) =

Probability of a randomly selected student wearing spectacles, P(A) =

Probability of a randomly selected student not wearing spectacles, P(B) =

Do the following activity -

Activity II : Decide the sample space yourself and fill in the following boxes.