The probabilities that players A and B of a team are selected for the captaincy for a tour…

Question

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4 , respectively. If $A$ is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected t...

Accepted Answer

Let

$A$ = event that player A is selected as captain

$B$ = event that player B is selected as captain

$W$ = event that the team wins the tournament

Given:

$P(A)=0.6,\, P(B)=0.4$

Also,

$P(W|A)=0.8,\, P(W|B)=0.7$

We have to find $P(W)$.

Using the formula of total probability:

$P(W)=P(A)\, P(W|A)+P(B)\, P(W|B)$

Substituting the values:

$P(W)=0.6	imes 0.8+0.4	imes 0.7$

$P(W)=0.48+0.28$

$P(W)=0.76$

So, the required probability is

$0.76$

Hence, the correct option is Option B.

Solutions · 1