English

A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.

Advertisements
Advertisements

Question

A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.

Sum
Advertisements

Solution

P(B|A) = `(P(B ∩ A))/(P(A)) = (P(A))/(P(A)) = 1`

A ∩ B = Φ i.e, P(A ∩ B) = P(Φ) = 0

⇒ P(B ∩ A) =`(P(B ∩ A))/(P(A)) = 0/(P(A)) = 0`

shaalaa.com
  Is there an error in this question or solution?
Chapter 13: Probability - Exercise 13.6 [Page 582]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 13 Probability
Exercise 13.6 | Q 1.2 | Page 582

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

A die is thrown three times. Events A and B are defined as below:
A : 5 on the first and 6 on the second throw.
B: 3 or 4 on the third throw.

Find the probability of B, given that A has already occurred.


Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).


If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find  P(A ∪ B)


If `P(A) = 6/11, P(B) = 5/11 "and"  P(A ∪ B) = 7/11` find

  1. P(A ∩ B)
  2. P(A|B)
  3. P(B|A)

Determine P(E|F).

A coin is tossed three times, where

E: head on third toss, F: heads on first two tosses


A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|F) and P (F|E)


An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple-choice question?


A and B are two events such that P (A) ≠ 0. Find P (B|A), if  A is a subset of B.


A card is drawn from a well-shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both? 


Bag A contains 4 white balls and 3 black balls. While Bag B contains 3 white balls and 5 black balls. Two balls are drawn from Bag A and placed in Bag B. Then, what is the probability of drawing a white ball from Bag B?


A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?


Two cards are drawn one after the other from a pack of 52 cards without replacement. What is the probability that both the cards drawn are face cards?


If A and B are two events such that P(A ∪ B) = 0.7, P(A ∩ B) = 0.2, and P(B) = 0.5, then show that A and B are independent


A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that exactly one of them will solve it?


The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If the oil had to be changed, what is the probability that a new oil filter is needed?


One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are white


A year is selected at random. What is the probability that it contains 53 Sundays


A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays


Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?


Choose the correct alternative:

A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is


Choose the correct alternative:

If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is


In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______ 


A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______


Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.


Find the probability that in 10 throws of a fair die a score which is a multiple of 3 will be obtained in at least 8 of the throws.


If P(A) = `1/2`, P(B) = 0, then `P(A/B)` is


Let A, B be two events such that the probability of A is `3/10` and conditional probability of A given B is `1/2`. The probability that exactly one of the events A or B happen equals.


It is given that the events A and B are such that P(A) = `1/4, P(A/B) = 1/2` and `P(B/A) = 2/3`, then P(B) is equal to ______. 


If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is ______.


If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.


If for any two events A and B, P(A) = `4/5` and P(A ∩ B) = `7/10`, then `P(B/A)` is equal to ______.


Three friends go to a restaurant to have pizza. They decide who will pay for the pizza by tossing a coin. It is decided that each one of them will toss a coin and if one person gets a different result (heads or tails) than the other two, that person would pay. If all three get the same result (all heads or all tails), they will toss again until they get a different result.

  1. What is the probability that all three friends will get the same result (all heads or all tails) in one round of tossing?
  2. What is the probability that they will get a different result in one round of tossing?
  3. What is the probability that they will need exactly four rounds of tossing to determine who would pay?

Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×