Algebra

Probability

Medium

core

'A' speaks the truth in 80% of the cases while 'B' in 90% of the cases. The probability that they contradict each other in stating the same statement is

$\frac{37}{50}$

$\frac{13}{50}$

$\frac{18}{25}$

$\frac{9}{25}$

✅ Correct Option: 2

A speaks the truth in 80% of cases, so A lies in 20% of cases.

B speaks the truth in 90% of cases, so B lies in 10% of cases.

P(A speaks truth) = $\frac{4}{5}$

P(A lies) = $\frac{1}{5}$

P(B speaks truth) = $\frac{9}{10}$

P(B lies) = $\frac{1}{10}$

A and B contradict each other when one speaks the truth and the other lies.

This happens in two cases:

A speaks truth and B lies
A lies and B speaks truth

For A speaks truth and B lies:

P(A speaks truth and B lies) = $\frac{4}{5} \times \frac{1}{10}$

$= \frac{4}{50}$

For A lies and B speaks truth:

P(A lies and B speaks truth) = $\frac{1}{5} \times \frac{9}{10}$

$= \frac{9}{50}$

Total probability of contradiction:

P(contradiction) = $\frac{4}{50} + \frac{9}{50}$

$= \frac{13}{50}$

Therefore, the probability that they contradict each other is $\frac{13}{50}$ .

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The mean of the number of heads in the two tosses of a coin is

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Let A and B be independent events such that $P(A) = \frac{3}{7}$ and $P(B) = \frac{1}{7}$ , Then

Match List-I with List-II

List-I	List-II
(A) P(A and B)	(I) $\frac{24}{49}$
(B) P(A or B)	(II) $\frac{18}{49}$
(C) P(A and not B)	(III) $\frac{25}{49}$
(D) P(neither A nor B)	(IV) $\frac{3}{49}$

Choose the correct answer from the options given below:

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A random variable X follow Poisson distribution such that P(X=1) = 2P(X=2) , then P(X=0) is

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If A and B are independent events, then which of the following is/are true?

(A) $\bar{A}$ and B are independent events

(B) $P(A \cap B) = 0$

(D) $P(A \cap B) = P(A) + P(B)$

Choose the correct answer from the options given below:

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The mean of the number of heads in a simultaneous toss of three coins is :

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In a game, a man wins Rs. 5 for getting a number greater than 4 and loses Rs. 1 otherwise, when a fair dice is thrown. The man decided to throw a die thrice but to quit as and when he gets a number greater than 4. The expected value of the amount(in Rs.) he wins or loses is:

'A' speaks the truth in 80% of the cases while 'B' in 90% of the cases. The probability that they contradict each other in stating the same statement is

Solution

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