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 OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.