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.
Practise Edexcel A Level Maths Statistical Distributions with exam-style questions for A Level Maths. 15 questions covering 6.1 Probability Distributions, 6.2 The Binomial Distribution, and 6.3 Cumulative Probabilities, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
