Question

Ram speaks the truth 3 out of 4 times while shyam speaks the truth 3 out of 5 times. What is the probability that they contradict each other?

Answer 1

n(s)=9

let a be the event when they contradict each other

n(a)=6

p(A)=n(a)/n(s)

=6/9

=2/3

Answer 2

Answer:

The probability that they contradict each other is 45%.

Step-by-step explanation:

Given : Ram speaks the truth 3 out of 4 times while shyam speaks the truth 3 out of 5 times.

To find : What is the probability that they contradict each other?

Solution :

Let A that Ram speaks truth.

Ram speaks the truth 3 out of 4 times i.e. $P(A)=\frac{3}{4}$

Let B that Shyam speaks truth

Shyam speaks the truth 3 out of 5 times i.e. $P(B)=\frac{3}{5}$

Let C that both speaks lie.

So, $P(A - C) = 1 - \frac{3}{4}=\frac{1}{4}$

$P(B- C) = 1 - \frac{3}{5}=\frac{2}{5}$

Now, A and B contradict each other

$=P(A)\times P(B-C) + P(B)\times P(A-C)$

$=\frac{3}{4}\times\frac{2}{5}+\frac{3}{5}\times\frac{1}{4}$

$=\frac{3}{10}+\frac{3}{20}$

$=\frac{6+3}{20}$

$=\frac{9}{20}$

Into percentage, $\frac{9}{20}\times 100=45\%$

Therefore, The probability that they contradict each other is 45%.