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Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive

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प्रश्न

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive

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उत्तर

P(A) = 0.4

P(A ∪ B) = 0.7

When A and B are mutually exclusive

P(A ∪ B) = P(A) P(B)

(i.e.,) 0.7 = 0.4 + P(B)

0.7 – 0.4 = P(B)

(i.e.,) P(B) = 0.3

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पाठ 12: Introduction to probability theory - Exercise 12.3 [पृष्ठ २५९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 12 Introduction to probability theory
Exercise 12.3 | Q 10. (i) | पृष्ठ २५९

संबंधित प्रश्‍न

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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.


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E: tail appears on one coin, F: one coin shows head


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E: no tail appears, F: no head appears


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


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?


In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.


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)


A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?


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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)

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