Mustafa plays a game where he can score 0, 5, 10, 15 or 20 points.
The random variable XXX, representing the number of points scored, has the following probability distribution, where aaa, b b\,b and k k\,k are constants.
| xxx | 0 | 5 | 10 | 15 | 20 |
| P(X=x)P(X=x)P(X=x) | aaa | kkk | bbb | 0.15 | 0.3 |
The probability of scoring more than 5 is three times the probability of scoring 5 or less.
Mustafa plays the game twice and adds the scores together. Each game is independent of the previous game.
Calculate, in terms of kkk, the probability that the total score is 25 points.
215 exam-style questions on Edexcel A Level Maths Statistical Distributions, covering 6.1 Probability Distributions, 6.2 The Binomial Distribution, and 6.3 Cumulative Probabilities. Each one has a worked solution and a mark scheme showing where the marks go.