Two pizza places in a college town advertise free, 30-minute delivery. Restauran

Question

Two pizza places in a college town advertise free, 30-minute delivery. Restaurant A makes its delivery on time 72 percent of the time, and Restaurant B makes its delivery on time 62 percent of the time. Suppose one pizza is ordered from each restaurant.

a.) If there is a 76 percent change that at least one of these restaurants delivers on time, find the probability that exactly one of the two will be delivered on time.

b.) If there is a 46 percent change that both pizzas are delivered on time, find the probability that neither of them will be delievered on time.

Show work.

Explanation / Answer

P(restaurant A makes it on time) = 0.72

P(restaurant B makes it on time) = 0.62

A) P(at least one of the restaurant makes it on time) = P(restaurant A makes it on time) + P(restaurant B makes it on time) - P(both restaurant makes it on time)

Or, 0.76 = 0.72 + 0.62 - P(both restaurant makes it on time)

Or, P(both restaurant makes it on time = 0.58

P(exactly one of two will be delivered on time) = P(restaurant A makes it on time) - P(both restaurant makes it on time) + P(restaurant B makes it on time) - P(both restaurant makes it on time)

= 0.72 - 0.58 + 0.62 - 0.58

= 0.18

B) P(both restaurant makes it on time) = 0.46

P(at least one of them will deliver on time) = P(restaurant A makes it on time ) + P(restaurant B makes it on time) - P(both restaurant makes it on time)

= 0.720+ 0.620 - 0.46

= 0.88

P(neither of them will be delivered on time) = 1 - P(at least one will deliver on time)

= 1 - 0.88

= 0.12

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.