Erik is investigating whether the number of goals scored by a football team in a game can be modelled using a binomial distribution. He uses the random variable X X\,X to denote the number of goals scored in a game and believes X∼B(2,0.5)X \sim B(2, 0.5)X∼B(2,0.5)
Using Erik's model, find P(X≥2)P(X \geq 2)P(X≥2)
The team play 40 games, find the expected number of games in which the team will score no goals.
Last season the team scored no goals in 9 out of 40 matches and scored 2 or more goals in 11 out of 40 matches. Explain whether or not your answers to part (a) and (b) support Erik's model.
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.