To get a complete collection of stamps, Ann needs to have 5 specific (and different) kinds of stamps, denoted by k1, ... k5 . She starts out with no stamps. She then receives 5 stamps randomly from a lottery. Each of these 5 stamps has probability 1/5 of being of any particular kind ki , and the kinds of the different stamps she receives are independent.

Note: Enter numerical answers; do not enter '!' or combinations.

1 What is the probability that Ann has a complete collection after receiving the 5 stamps from the lottery?

2 Given that Ann does not have a complete collection after receiving the 5 stamps from the lottery, what is the probability that she is missing exactly one stamp?

Anyone has any answer?

96/401

1 To calculate the probability that Ann has a complete collection after receiving the 5 stamps from the lottery, we need to consider the different ways she can obtain the 5 specific kinds of stamps.

There are a total of 5! = 5 * 4 * 3 * 2 * 1 = 120 possible arrangements of the 5 stamps.

Out of these arrangements, only one arrangement represents a complete collection of stamps.

Therefore, the probability that Ann has a complete collection after receiving the 5 stamps from the lottery is 1/120.

2 Given that Ann does not have a complete collection after receiving the 5 stamps from the lottery, we need to calculate the probability that she is missing exactly one stamp.

To find this probability, we first need to determine the number of ways Ann can be missing exactly one stamp. There are 5 possible stamps that could be missing, so there are 5 ways Ann can be missing exactly one stamp.

The total number of possible arrangements of the 5 stamps is still 120.

Therefore, the probability that Ann is missing exactly one stamp, given that she does not have a complete collection, is 5/120, which simplifies to 1/24.