# Question In a sales campaign, a company gives each customer who buys its magazine a picture card. There are 10 different pictures and any customer who collects a complete set of all 10 picture cards gets a free gift. On any occasion when a customer buys a magazine, the card received is equally likely to be any of the 10 picture cards. (i) Find the probability that the first 4 cards the customer receives all carry different pictures. (ii) Find the probability that the first 4 cards received result in the customer having exactly 3 different pictures. (iii) Two of the 10 pictures are X and Y. Find the probability that the first 4 cards received result in the customer having a picture of X or of Y (or both). (iv) At a certain stage the customer has collected 9 of the 10 pictures. Find the least value of n such that the probability of at most n more cards are needed to complete the set is at least 0.99.

Z8GWBP The Asker · Probability and Statistics

In a sales campaign, a company gives each customer who buys its magazine a picture card. There are 10 different pictures and any customer who collects a complete set of all 10 picture cards gets a free gift. On any occasion when a customer buys a magazine, the card received is equally likely to be any of the 10 picture cards.

(i) Find the probability that the first 4 cards the customer receives all carry different pictures.

(ii) Find the probability that the first 4 cards received result in the customer having exactly 3 different pictures.

(iii) Two of the 10 pictures are X and Y. Find the probability that the first 4 cards received result in the customer having a picture of X or of Y (or both).

(iv) At a certain stage the customer has collected 9 of the 10 pictures. Find the least value of n such that the probability of at most n more cards are needed to complete the set is at least 0.99.

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