1. ## Probability

Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of orders shipped to the person making the order.

A) What is the probability that a randomly selected order will be gift wrapped and sent to another person?

B) What is the probability that a randomly selected order will be gift wrapped?

Thanks to all who respond and taking your time!

2. Originally Posted by redschaf
Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of orders shipped to the person making the order.

A) What is the probability that a randomly selected order will be gift wrapped and sent to another person?

B) What is the probability that a randomly selected order will be gift wrapped?

Thanks to all who respond and taking your time!
Let $O$ be the event that an order is sent to the buyer and $\hat{O}$ be the event that the order is sent to someone else. Similiarly, let $G$ represent the event that a gift is wrapped and $\hat{G}$ the event that a gift is not wrapped.

We are given,

$P(O)=0.7$, $P(\hat{O})=0.7$, $P(G|O)=0.1$, and $P(G|\hat{O})=0.6$.

a) We want to find the intersection of two events; namely,

$P(G\cap\hat{O})=P(G|\hat{O})P(\hat{O})=0.18$

b) We want the total probability of selecting a wrapped gift, which is

$P(G)=P(G|O)P(O)+P(G|\hat{O})P(\hat{O})$