In a mechanical device it is know that part 1 works 65 of th

In a mechanical device it is know that part 1 works 65% of the time, and

part 2 works 50% of the time. Parts 1 and 2 both work 18% of the time.

What is the probability that part 1 or part 2 will work in this device?

What is the probability that part 1 works only or part 2 works only?

Solution

What is the probability that part 1 or part 2 will work in this device?

P(part 1)=0.65 P(part 2)=0.50 , P(1n 2)=0.18

P(A uB)=P(A)+P(B)-P(AnB)=0.65+0.50-0.18=0.97

b) the probability that part 1 works only or part 2 works only

P(A or B) = P(A only) + P(B only) + P(A and B)

=1-0.65+1-0.50-0.18=0.67