ē¬¬2/2é Question 1 (14 marks)
A mystery toy box contains one of the 12 kinds of toys in a set of newly released toys, where 4 of
them are rabbits. Any purchase made costs $10. Assume that the kinds of toys in the box are
independent and the probability of obtaining each kind of toy is the same.
(a) Suppose Karen has 4 purchases on the mystery toy box.
(i) What is the probability that exactly 3 toys are rabbits?
(ii) What is the expected number of toys which are rabbits?
(b) If Karen obtains at least two toys which are not rabbits after spending $40, she will stop having
purchases on the mystery toy box. Find the probability that Karen will stop making purchases
on the mystery toy box after spending $40.
(c) Karen and her 5 friends each spend $40 on the mystery toy box. What is the probability that
none of them obtain exactly 3 rabbits?