हिंदी

If P(A) = 45, and P(A ∩ B) = 710, then P(B|A) is equal to ______.

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • `1/10`

  • `1/8`

  • `7/8`

  • `17/20`

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

If P(A) = `4/5`, and P(A ∩ B) = `7/10`, then P(B|A) is equal to `7/8`.

Explanation:

Given that: P(A) = `4/5`, and P(A ∩ B) = `7/10`

∴ P(B|A) = `("P"("A" ∩ "B"))/("P"("A"))`

= `(7/10)/(4/5)`

= `7/8`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 13: Probability - Exercise [पृष्ठ २७९]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 13 Probability
Exercise | Q 56 | पृष्ठ २७९

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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.

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


Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`


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)

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?


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 P(A) = `1/2`,  P(B) = 0, then P(A|B) is ______.


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? 


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.


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?


In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in at least one subject?


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


Can two events be mutually exclusive and independent simultaneously?


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


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 mutually exclusive


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


Choose the correct alternative:

Let A and B be two events such that `"P"(bar ("A" ∪ "B")) = 1/6, "P"("A" ∩ "B") = 1/4` and `"P"(bar"A") = 1/4`. Then the events A and B are


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


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


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 ______. 


Read the following passage:

Recent studies suggest the roughly 12% of the world population is left-handed.

Depending upon the parents, the chances of having a left-handed child are as follows:

A :  When both father and mother are left-handed:
Chances of left-handed child is 24%.
B :  When father is right-handed and mother is left-handed:
Chances of left-handed child is 22%.
C :  When father is left-handed and mother is right-handed:
Chances of left-handed child is 17%.
D :  When both father and mother are right-handed:
Chances of left-handed child is 9%.

Assuming that P(A) = P(B) = P(C) = P(D) = `1/4` and L denotes the event that child is left-handed.

Based on the above information, answer the following questions:

  1. Find `P(L/C)` (1)
  2. Find `P(overlineL/A)` (1)
  3. (a) Find `P(A/L)` (2)
    OR
    (b) Find the probability that a randomly selected child is left-handed given that exactly one of the parents is left-handed. (2)

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) =


If A and B are events and \[P(B) \neq 0\], which expression gives \[P(A \mid B)\]?


Which statement is the multiplication rule for two events A and B?


For \[E=\{(b,b)\}\] and \[F=\{(b,b),(g,b),(b,g)\}\], what are \[E\cap F\], \[P(E\cap F)\], and \[P(F)\]?


Which conditional probabilities are equal to 1 when \[P(F)\neq 0\]?


If A and B are any two events of S and \[P(F)\neq 0\], which formula is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×