- #1
CAF123
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Homework Statement
Suppose that you continually collect coupons and that there are m different types. Suppose also that each time a new coupon is obtained, it is a type i coupon with probability [itex] p_{i} [/itex], i = 1,.. m. Suppose you have just collected your n th coupon. What is the probability that it is a new type?
Hint: condition on the type of coupon
The Attempt at a Solution
I said that after (n-1) collected coupons, the prob that you collected a specific coupon is (1/m)^(n-1) => the prob that you didn't collect a specific coupon was (1-(1/m))^(n-1).
I also let [itex] A_{i}[/itex] be the event that a new coupon was collected on collection i and I wanted to determine [itex] P(A_{n})[/itex] but I ddn't get very far with this approach.
I am unsure of what to try next.
Thanks