Question

You play soccer, and want to be the Goalkeeper, but that depends who is the Coach...

You play soccer, and want to be the Goalkeeper, but that depends who is the Coach today: with Coach Sam the probability of being Goalkeeper is 0.6 with Coach Alex the probability of being Goalkeeper is 0.4 Sam is Coach more often, about 6 out of every 10 games (a probability of 0.6). So, what is the probability you will be a Goalkeeper today?

please type it do not handwritten

Math   Statistics-And-Probability   
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Answer #1

Let, event S denotes that coach Sam will be the coach today and event A denotes that coach Alex will be the coach today.

Also, event G denotes that I will be a goalkeeper today.

From, the given information in question the probability of the events are :

P(S) = 0.6 P(A)= 0.4

P(G | S) = probability of being goalkeeper when coach Sam is there = 0.6

P(G | A) = probability of being goalkeeper when coach Alex is there = 0.4

Here, S and A are mutually exclusive events, whose probabilities sum to unity, then by the theorem of total probability, we will calculate P(G).

P(G) = P(G | S)*P(S) + P(G | A)*P(A) = 0.6*0.6 + 0.4*0.4 = 0.52

Therefore, the probability that I will be a Goalkeeper today is 0.52

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