A bridal shop is slow with deliveries. If Karen orders her dress 6 months before her...

A bridal shop is slow with deliveries. If Karen orders her dress 6 months before her rehearsal dinner, there is a 75% chance that the dress will arrive on time for her rehearsal dinner. If Karen forgets to order her dress 6 months early, there is only a 20% chance that the dress will arrive on time for her rehearsal dinner. Because Karen is so busy planning her wedding, she estimates that there is only a 90% chance that she remembers to order her dress 6 months early.

a) What is the probability that the dress arrives on time for Karen's rehearsal dinner?

b) If the dress arrives on time, what is the probability that Karen forgot to order her dress 6 months early?

Solutions

Expert Solution

First, I defined the events clearly and wrote the given probabilities in terms of these events.

For part a), I used Law of Total Probability

If is an event and is a partition of the sample space,

then . Here and forms a partition of the sample space.

For part b) I used the Bayes Rule,

orchestra answered 1 year ago

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