Amy and Kenneth are playing a game consisting of two rounds. In the first round,

Question

Amy and Kenneth are playing a game consisting of two rounds. In the first round, Amy and Kenneth are required to draw a ball from a black box containing 3 red balls and 7 blue balls initially without replacement. Only the player who draws the first red ball can enter the second round. Amy plays first. (2 marks) (a) Find the probability that Amy can enter the second round. (b) In the second round, the player first shouts out a positive integer n and then presses a button in the computer repeatedly and the computer will give an output either ‘A' or 'B' every time. Ifthe computer gives A' in a press, the probability that it gives 'A' in the next press is 0.92. If the computer gives .B, in a press, the probability that it gives 'A' in the next press is 0.12. If the computer gives 'A' in neither the n th press nor the 2nh press, the player can get a prize. It is given that the computer gives A' in the first press. 0) Let m be a positive integer. Express the probability that the computer gives 'A' in the m press in terms of m. Using the method of completing square, find the value of n maximum possible probability of getting a prize. (ii) such that the player has the (ii) It is given that the player always shouts out the value of n such that he or she has the maximum possible probability of getting a prize. Kenneth claims that the probability that Amy cannot win a prize in the game exceeds 0.8. Do you agree with his claim? Explain your answer briefly (11 marks)

Explanation / Answer

(a) In the first draw, the probability that amy draws the red ball is, P=3/10.

To enter the second round in first draw, the probability is 3/10.

In second draw, the probability will be, 3/8. (as the number of ball reduces in each draw, and the kenneth also draw after amy so it reduces by 2)

In third draw, the probability will be 3/6 and goes on...

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