One fifth of all bars of a certain brand of chocolate contain a free ticket to go to a concert. The chocolate bars cost 60p each and the tickets cost £5 each. Six friends wish to go to the concert. They buy bars of the chocolate until they have six tickets. Let X be the number of bars they buy. (a) State the distribution of X. (b) Find the probability that the friends will buy exactly 29 bars. (c) Find the difference between the amount the friends expect to pay using their strategy and the amount they would pay if they just bought the tickets. (d) Find the probability that the friends will pay more using this strategy than if they had just bought the tickets.
I have done parts a and c correctly but I can’t get the right answer for b or d.
For b I have done X~NB(6,0.2) P(X=29)=(28C5)(0.2)^6(0.8)^17 = 0.1416 (4sf) but the correct answer is 0.0371
And I’m not sure where to start d as I thought that it would be P(X>30) but I can’t do cumulative probability with the negative binomial distribution.