Arun
Last Activity: 4 Years ago
Now, the ball drawn may be black or non-black (any of the remaining 5 different colours) and both may say that it is black.
Let C = event that the ball drawn is black and both agreeing that it is black
P(C)=
6
1
×
3
2
×
5
4
=
45
4
Let D = event that the ball drawn is non-black (any of the remaining 5 different colours) and both agreeing that it is black but telling a lie.
Both can tell a lie in 5 different ways.
Suppose the non- black ball drawn is blue, they may say it is black, white,red,yellow,green (all lies) of which probability of telling black is
5
1
on which they agree.
A may tell a lie that it is black in
5
1
×
3
1
=
15
1
ways.
B can tell it in
5
1
×
5
1
=
25
1
ways.
Also there is
6
5
probability of picking up a non-black ball.
Thus, probability that a non-black ball is drawn and both agree that it is black thus asserting that it is black but telling a lie is
P(D)=
6
5
×
15
1
×
25
1
=
450
1
Now, we have found probability of two events in which both are asserting that the ball is black, but when event C occurs the assertion is with speaking the truth and when event D occurs, assertion is by telling a lie.
The probability of their asserting that the ball is black and speaking truth
=
P(C)+P(D)
P(C)
=
45
4
+
450
1
45
4
=
41
40
