Question

When a customer places an order at Derin's bakery, there is an 85% probability that the order will include some kind of dessert. One day, 7 customers place orders at Derin's bakery. Assuming that each order is equally likely to include dessert, what is the probability that at least order will not include dessert? Round your answer to the nearest hundredth.

Answer 1

Answer:

0.68

Step-by-step explanation:

The probability that the order will include some kind of dessert is $p=0.85$ and the probability that the order will not include some kind of dessert is $q=1-p=1-0.85=0.15.$

First, find the probability that all 7 orders include some kind of dessert:

$Pr_1=C_7^7p^7q^{7-7}=p^7=(0.85)^7.$

Then the probability that at least order will not include dessert is

$Pr_2=1-Pr_1=1-(0.85)^7\approx 0.68$