A game consists of rolling a fair six‑sided die. Each time a 6 is rolled the player wins £10; otherwise the player loses £2. The game is played 15 independent times. Let $Y$ be the total profit after the 15 rolls. (a) Find the probability that the player makes a profit (i.e., $Y0$). (b) Find the expected profit and the standard deviation of $Y$. Give the probability as a decimal to three decimal places, and the expected profit and standard deviation to two decimal places.

Question

A game consists of rolling a fair six‑sided die. Each time a 6 is rolled the player wins £10; otherwise the player loses £2. The game is played 15 independent times. Let $Y$ be the total profit after the 15 rolls. (a) Find the probability that the player makes a profit (i.e., $Y>0$). (b) Find the expected profit and the standard deviation of $Y$. Give the probability as a decimal to three decimal places, and the expected profit and standard deviation to two decimal places.

Accepted Answer

Probability 0.468; Expected profit £0.00; Standard deviation £17.32

Igcse Model Questions Vol1 2021 Mathematics Question 8

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