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 a a\,a and b b\,b are constants.
| xxx | 0 | 5 | 10 | 15 | 20 |
| P(X=x)P(X=x)P(X=x) | aaa | 0.2 | 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 the probability that the total score is 25 points.
390 exam-style questions on AQA A Level Maths 2.4 N: Statistical distributions, covering 2.4.1 Discrete distributions and the binomial, 2.4.2 The Normal distribution (A-level only), and 2.4.3 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.