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.

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?

totally lost!!

1. 0.0384 (5!/5^5)

2. ???

Anyone know answer to 2?

2)

0.4096

To solve these probability questions, we can use the concept of combinations.

1. To find the probability that Ann has a complete collection after receiving the 5 stamps from the lottery, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

- Total number of possible outcomes: There are 5 random stamps that Ann receives, and each stamp can be of any of the 5 different kinds (ki). So, there are 5^5 = 3125 possible outcomes.

- Number of favorable outcomes: To have a complete collection, Ann needs to have 5 specific and different kinds of stamps. Since she starts with no stamps, she needs to receive each of the 5 kinds of stamps in the lottery. The probability of obtaining a specific kind of stamp is 1/5, and since the stamps are independent, the probability of receiving all 5 kinds of stamps is (1/5)^5.

Therefore, the probability that Ann has a complete collection is:
Number of favorable outcomes / Total number of possible outcomes = (1/5)^5 / 3125 = 1/3125.

2. To find the probability that Ann is missing exactly one stamp given that she does not have a complete collection after receiving the 5 stamps from the lottery, we need to calculate the number of favorable outcomes and the total number of possible outcomes.

- Total number of possible outcomes: Since Ann does not have a complete collection, she can be missing one or more stamps. The total number of possible outcomes is the number of ways Ann can receive 5 stamps that are not a complete collection. This can be calculated as the sum of the number of ways of choosing 1, 2, 3, 4 stamps to be missing, respectively.

- Number of favorable outcomes: To find the number of favorable outcomes, we want to count the number of ways Ann can be missing exactly one stamp. This can be calculated by choosing any one of the 5 kinds of stamps to be missing, and then choosing 4 stamps out of the remaining 4 kinds. This can be expressed as 5 * (4 choose 4), where (4 choose 4) represents the number of ways of choosing 4 stamps out of 4.

Therefore, the probability that Ann is missing exactly one stamp is:
Number of favorable outcomes / Total number of possible outcomes = 5 * (4 choose 4) / Total number of possible outcomes.

Note: "n choose k" is the notation used to represent the number of ways of choosing k items from a set of n items, and can be calculated as n! / (k! * (n - k)!), where "!" denotes factorial.