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?

C) Is gift wrapping independent of the destination of the gift?

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?

C) Is gift wrapping independent of the destination of the gift?

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

We are given,

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

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

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

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

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