If Ram tells truth 4 times out of 5
and Shyam tells truth 3 times out
of 4. The probability that both of
them contradict each other is?
Answers
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}P(A)=
4
3
Let B that Shyam speaks truth
Shyam speaks the truth 3 out of 5 times i.e. P(B)=\frac{3}{5}P(B)=
5
3
Let C that both speaks lie.
So, P(A - C) = 1 - \frac{3}{4}=\frac{1}{4}P(A−C)=1−
4
3
=
4
1
P(B- C) = 1 - \frac{3}{5}=\frac{2}{5}P(B−C)=1−
5
3
=
5
2
Now, A and B contradict each other
=P(A)\times P(B-C) + P(B)\times P(A-C)=P(A)×P(B−C)+P(B)×P(A−C)
=\frac{3}{4}\times\frac{2}{5}+\frac{3}{5}\times\frac{1}{4}=
4
3
×
5
2
+
5
3
×
4
1
=\frac{3}{10}+\frac{3}{20}=
10
3
+
20
3
=\frac{6+3}{20}=
20
6+3
=\frac{9}{20}=
20
9
Into percentage, \frac{9}{20}\times 100=45\%
20
9
×100=45%
Therefore, The probability that they contradict each other is 45%.