# Question 7 In a sales campaign, a petrol company gives a each motorist who buys their petrol a card with a picture of a film star on it. There are 10 different pictures, one each of 10 different film stars, and any motorist who collects a complete set of all 10 pictures gets a free gift. On any occasion when a motorist buys petrol, the card received is equally likely to carry any one of the 10 pictures in the set. (i) Find the probability that the first four cards the motorist receives all carry different pictures. (ii) Find the probability that the first four cards received result in the motorist having exactly three different pictures. (iii) Two of the ten film stars in the set are X and Y. Find the probability that the first four cards received result in the motorist having a picture of X or Y (or both). (iv) At a certain stage the motorist has collected nine of the ten pictures. Find the least value of n such that P(at most n more cards are needed to complete the set) > 0.99. (UCLES)

BKKN3U The Asker · Probability and Statistics

Transcribed Image Text: 7 In a sales campaign, a petrol company gives a each motorist who buys their petrol a card with a picture of a film star on it. There are 10 different pictures, one each of 10 different film stars, and any motorist who collects a complete set of all 10 pictures gets a free gift. On any occasion when a motorist buys petrol, the card received is equally likely to carry any one of the 10 pictures in the set. (i) Find the probability that the first four cards the motorist receives all carry different pictures. (ii) Find the probability that the first four cards received result in the motorist having exactly three different pictures. (iii) Two of the ten film stars in the set are X and Y. Find the probability that the first four cards received result in the motorist having a picture of X or Y (or both). (iv) At a certain stage the motorist has collected nine of the ten pictures. Find the least value of n such that P(at most n more cards are needed to complete the set) > 0.99. (UCLES)
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Transcribed Image Text: 7 In a sales campaign, a petrol company gives a each motorist who buys their petrol a card with a picture of a film star on it. There are 10 different pictures, one each of 10 different film stars, and any motorist who collects a complete set of all 10 pictures gets a free gift. On any occasion when a motorist buys petrol, the card received is equally likely to carry any one of the 10 pictures in the set. (i) Find the probability that the first four cards the motorist receives all carry different pictures. (ii) Find the probability that the first four cards received result in the motorist having exactly three different pictures. (iii) Two of the ten film stars in the set are X and Y. Find the probability that the first four cards received result in the motorist having a picture of X or Y (or both). (iv) At a certain stage the motorist has collected nine of the ten pictures. Find the least value of n such that P(at most n more cards are needed to complete the set) > 0.99. (UCLES)