Question

Jeremy designs a game for a school fair. He has two 5-sided spinners. The spinners are equally likely to land on each of their sides. One spinner has 2 red sides, 1 green side, and 2 blue sides. The other spinner has 3 red sides, 1 yellow side, and 1 blue side.

(a) Calculate the probability that the two spinners will land on the same color.

The game consists of spinning each spinner once. It costs 20p to play the game. To win a prize, both spinners must land on the same color. The prize for a win is 50p. 100 people play the game.

(b) Work out an estimate of the profit that Jeremy should expect to make.

Answer 1

The probability that both spinners land on the same color is found by summing the individual probabilities for each color that appears on both spinners. Jeremy expects to make a profit of 400p after 100 people play his game, considering the cost to play and the prize awarded.

Step-by-step explanation:

To calculate the probability that the two spinners will land on the same color, we must consider the chance of each color coming up on both spinners. Since one spinner has 2 red sides, 1 green side, and 2 blue sides, and the other has 3 red sides, 1 yellow side, and 1 blue side, we can calculate the combined probabilities of these events occurring simultaneously. The probability of both spinners landing on red is ³2/5 * 3/5 = 6/25. For blue, it's ³2/5 * 1/5 = 2/25. And they cannot both land on green or yellow because these colors don't appear on both spinners.

To estimate Jeremy's expected profit from the game when 100 people play, we consider the cost per play (20p) and the prize (50p). Let's calculate the expected number of wins first, which is 100 times the probability of winning (landing on the same color). The expected number of wins is 100 * (6/25 + 2/25) = 100 * 8/25 = 32. Therefore, Jeremy expects to pay out 32 * 50p = 1600p in prizes. The total amount taken in for 100 games is 100 * 20p = 2000p. Subtracting the prizes, Jeremy's profit is 2000p - 1600p = 400p.