10 Consider the two spinners illustrated: pentagonal square spinner spinner Al- R R R' a Copy and complete the tree diagram which shows all possible results when the two spinners are R' R spun together. R' b Calculate the probability that exactly one red will occur. The pair of spinners is now spun 10 times. Let X be the number of times that exactly one red occurs. i State the distribution of X. ii Write down expressions for P(X = 1) and P(X =9). Hence determine which of these outcomes is more likely.1 Lakshmi rolls a regular six-sided die. She wins twice the number of dollars as the number rolled. I How much dines Iakshmi expect to win from one roll of the die? 5 If it costs $8 to play the game, would you advise Lakshmi to play many games? Explain your answer. 10 Caleb is thrown a baseball 4 times. Let X be the number of times Caleb catches the ball. The probability distribution of X is: 0 1 2 3 4 P(X = =) 0.1 0.2 0.3 0.3 0.1 a Find E(X). b Let Y be the number of times Caleb drops the ball. Find E(Y). 11 The spinner alongside is spun 20 times. Let X be the number of threes spun. 5 a Explain why X is a binomial random variable. b Find the mean and standard deviation of X. 4 2 310 Suppose X is normally distributed with mean 25 and standard deviation 6. Find k such that: a P(X k) = 0.4 c P(20 5.4) = P(Z > -1.7), find the mean of X