Question

Dr craft is playing a game where he has to pass through two gates to win a prize the probability of the first gate open is 0.2 well the probability of the second gate open is 30% and both gates open at the same time 10% of the time what is the probability that both gates will be closed when Dr craft gets there?

Answer 1

The event that both doors won't open is the complement of the event that at least one will open, and this event is the union of the event that door A will open and the event that door B will open, so

`P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.2+0.3-0.1=0.4`

so if we want both doors to be closed it is the complement of the previous probability

`1-0.4=0.6`

so the probability of both doors being closed is 0.6