A discrete mathematics problem by Syed Baqir

Discrete Mathematics Level pending

You are off to soccer, and want to be the Goalkeeper, but that depends who is the Coach today:

With Coach Sam the probability of being Goalkeeper is 0.5 with Coach Alex the probability of being Goalkeeper is 0.3 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?

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