English

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

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

P (B|A) = `(P (A cap B))/(P (A))`

`= (P (A))/(P(A)) = 1`          ...(∵ A ⊂ B ⇒ A ∩ B = A)

A is a subset of set B.

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 1.1 | Page 582

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Assume that each born child 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

  1. the youngest is a girl.
  2. at least one is a girl.

The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive


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: at most two tails, F: at least one tail


Determine P(E|F).

A die is thrown three times,

E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses


Determine P(E|F).

Mother, father and son line up at random for a family picture

E: son on one end, F: father in middle


A black and a red dice are rolled. 

Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.


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


Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.


If A and B are events such as that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`, then find

1) P(A / B)

2) P(B / A)


An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is repeated. Find the probability that the third ball is drawn is black.


A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.


If events A and B are independent, such that `P(A)= 3/5`,  `P(B)=2/3` 'find P(A ∪ B).


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?


From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when the first card drawn is replaced in the pack


If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)


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 the problem is solved?


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


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 one white and one black


Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events


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, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are `3/4, 1/2, 5/8`. The probability that the target is hit by A or B but not by C 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 ______ 


Let A and B be two events. If P(A) = 0.2, P(B) = 0.4, P(A ∪ B) = 0.6, then P(A|B) is equal to ______.


If P(A ∩ B) = `7/10` and P(B) = `17/20`, then P(A|B) equals ______.


If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.


Two cards are drawn out randomly from a pack of 52 cards one after the other, without replacement. The probability of first card being a king and second card not being a king is:


If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:


A bag contains 6 red and 5 blue balls and another bag contains 5 red and 8 blue balls. A ball is drawn from the first bag and without noticing its colour is placed in the second bag. If a ball is drawn from the second bag, then find the probability that the drawn ball is red in colour.


A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.


If A and B are two events such that P(A) = `1/3`, P(B) = `1/5` and P(A ∪ B) = `1/2`, then P(A|B') + P(B|A') is equal to ______.


For a biased dice, the probability for the different faces to turn up are

Face 1 2 3 4 5 6
P 0.10 0.32 0.21 0.15 0.05 0.17

The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is ______.


Students of under graduation submitted a case study on “Understanding the Probability of Left-Handedness in Children Based on Parental Handedness”. Following Recent studies suggest that roughly 12% of the world population is left-handed. Depending on the parents’ handedness, the chances of having a left-handed child are as follows:

Scenario A: Both parents are left-handed, with a 24% chance of the child being left-handed.

Scenario B: The fathers is right-handed and the mothers left-handed, with a 22% chance of child being left-handed.

Scenario C: The fathers left-handed and the mother is right-handed, with a 17% chance of child being left-handed.

Scenario D: Both parents are right-handed, with a 9% chance of having a left-handed child.

Assuming that scenarios A, B, C and D are equally likely and L denotes the event that the child is left-handed, answer the following questions.

  1. What is the overall probability that a randomly selected child is left-handed?
  2. Given that exactly one parent is left-handed, what is the probability that a randomly selected child is left-handed?
  3. If a child is left-handed, what is the probability that both parents are left-handed?

If P(B) = `3/5`, P(A | B) = `1/2` and P(A ∪ B) = `4/5`, then P(A ∪ B) + P(A' ∪ B) =


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×