Advertisements
Advertisements
Question
From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24 is
Options
6/25
1/4
1/6
2/5
None of these
Solution
Number divisible by 6 between 1 to 100 = 16
Number divisible by 8 between 1 to 100 = 12
Number divisible by 6 and 8 between 1 to 100 = 4
Number divisible by 24 between 1 to 100 = 4
P(number divisible by 6 or 8) = P(number divisible by 6) + P(number divisible by 8) - P(number divisible by 6 and 8)
\[= \frac{16}{100} + \frac{12}{100} - \frac{4}{100}\]
\[ = \frac{24}{100}\]
\[ = \frac{6}{25}\]
P(number divisible by 6 or 8 but not by 24) = P(number divisible by 6 or 8) - P(number divisible by 24)
\[= \frac{6}{25} - \frac{4}{100}\]
\[ = \frac{6}{25} - \frac{1}{25}\]
\[ = \frac{5}{25}\]
\[ = \frac{1}{5}\]
APPEARS IN
RELATED QUESTIONS
In a set of 10 coins, 2 coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides.
How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?
Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?
Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?
A couple has two children. Find the probability that both the children are (i) males, if it is known that at least one of the children is male. (ii) females, if it is known that the elder child is a female.
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that both are kings .
A bag contains 20 tickets, numbered from 1 to 20. Two tickets are drawn without replacement. What is the probability that the first ticket has an even number and the second an odd number.
If A and B are two events such that P (A ∩ B) = 0.32 and P (B) = 0.5, find P (A/B).
A pair of dice is thrown. Find the probability of getting 7 as the sum if it is known that the second die always exhibits a prime number.
A card is drawn from a pack of 52 cards so the teach card is equally likely to be selected. In which of the following cases are the events A and B independent?
A = The card drawn is a king or queen, B = the card drawn is a queen or jack.
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (A/B) .
A die is tossed twice. Find the probability of getting a number greater than 3 on each toss.
An anti-aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?
A die is thrown thrice. Find the probability of getting an odd number at least once.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red, (ii) first ball is black and second is red, (iii) one of them is black and other is red.
The probabilities of two students A and B coming to the school in time are \[\frac{3}{7}\text { and }\frac{5}{7}\] respectively. Assuming that the events, 'A coming in time' and 'B coming in time' are independent, find the probability of only one of them coming to the school in time. Write at least one advantage of coming to school in time.
Two dice are thrown together and the total score is noted. The event E, F and G are "a total of 4", "a total of 9 or more", and "a total divisible by 5", respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.
Let A and B be two independent events such that P(A) = p1 and P(B) = p2. Describe in words the events whose probabilities are: `1 - (1 - p_1 )(1 -p_2 ) `
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and other is red.
Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?
A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is the probability that both of them will be selected ?
Three cards are drawn with replacement from a well shuffled pack of 52 cards. Find the probability that the cards are a king, a queen and a jack.
There are 3 red and 5 black balls in bag 'A'; and 2 red and 3 black balls in bag 'B'. One ball is drawn from bag 'A' and two from bag 'B'. Find the probability that out of the 3 balls drawn one is red and 2 are black.
A bag contains 4 white and 5 black balls and another bag contains 3 white and 4 black balls. A ball is taken out from the first bag and without seeing its colour is put in the second bag. A ball is taken out from the latter. Find the probability that the ball drawn is white.
When three dice are thrown, write the probability of getting 4 or 5 on each of the dice simultaneously.
If A and B are two independent events such that P (A) = 0.3 and P (A ∪ \[B\]) = 0.8. Find P (B).
If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of Aand B occurs) = \[\frac{5}{9}\], then find the value of p.
A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is
Two dice are thrown simultaneously. The probability of getting a pair of aces is
Choose the correct alternative in the following question:
If A and B are two events associated to a random experiment such that \[P\left( A \cap B \right) = \frac{7}{10} \text{ and } P\left( B \right) = \frac{17}{20}\] , then P(A|B) =
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3}, P\left( A|B \right) = \frac{1}{4}, \text{ then } P\left( A \cap B \right) \text{ equals} \]
Mark the correct alternative in the following question: A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability that exactly two of the three balls were red, the first ball being red, is
Mark the correct alternative in the following question:
In a college 30% students fail in Physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she failed in Mathematics is
Mark the correct alternative in the following question
Three persons, A, B and C fire a target in turn starting with A. Their probabilities of hitting the target are 0.4, 0.2 and 0.2, respectively. The probability of two hits is
Mark the correct alternative in the following question:
Two dice are thrown. If it is known that the sum of the numbers on the dice was less than 6, then the probability of getting a sum 3, is
The probability that in a year of 22nd century chosen at random, there will be 53 Sunday, is ______.
An insurance company insured 3000 cyclists, 6000 scooter drivers, and 9000 car drivers. The probability of an accident involving a cyclist, a scooter driver, and a car driver are 0⋅3, 0⋅05 and 0⋅02 respectively. One of the insured persons meets with an accident. What is the probability that he is a cyclist?
Refer to Question 6. Calculate the probability that the defective tube was produced on machine E1.
