Question

The probability that A speaks truth is 4/5, while this probability for B is 3/4.The probability that they contradict each other when asked to speak on an event is.....,Select Proper option from the given options.
(a) 7/20
(b) 1/5
(c) 3/20
(d) 4/5

Answer 1

Answer:

Option A (7/20) is correct.

Step-by-step explanation:

The probability that A speaks truth is P(A) =4/5

The probability that A speaks lie is

P(A') =1/5

The probability that B speaks truth is

P(B) =3/4

The probability that B speaks lie is

P(B') =1/4

The probability that they contradict each other when asked to speak on an event is P(C)=P(A)P(B')+P(B)P(A')

$= \frac{4}{5} \times \frac{1}{4} + \frac{3}{4} \times \frac{1}{5} \\ \\ = \frac{4}{20} + \frac{3}{20} \\ \\ = \frac{7}{20}$

Option A is correct.

Hope it helps you.

Answer 2

Option A - The probability that they contradict each other when asked to speak on an event is  $\dfrac{7}{20}$.

Step-by-step explanation:

Given : The probability that A speaks truth is $\frac{4}{5}$, while this probability for B is $\frac{3}{4}$.

To find : The probability that they contradict each other when asked to speak on an event ?

Solution :

The probability that A speaks truth is $P(A)=\frac{4}{5}$

The probability that A speaks lie is $P(A')=1-P(A)$

$P(A')=1-\frac{4}{5}$

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

The probability that B speaks truth is $P(B)=\frac{3}{4}$

The probability that B speaks lie is $P(B')=1-P(B)$

$P(B')=1-\frac{3}{4}$

$P(B')=\frac{1}{4}$

The probability that they contradict each other when asked to speak on an event is given by,

$P(C)=P(A)P(B')+P(B)P(A')$

Substitute the value,

$P(C)= \frac{4}{5} \times \frac{1}{4} + \frac{3}{4} \times \frac{1}{5}$

$P(C)= \frac{4}{20} +\frac{3}{20}$

$P(C) = \frac{7}{20}$

Therefore, option A is correct.

#Learn more

If a speaks the truth 60% of the times, b speaks the truth 50% of the times. What is the probability that at least one will tell the truth?

https://brainly.in/question/8381969