Please explain all A, B, C , and D

A random variable X has a probability distribution given in the following table. 1 2 P(X = 1) P 15 (a) Given that E(.X) = 0.8. find the exact value of: (i) q: 2 15 0(p ) +75+ 29 = 0.8 (ii) p. P = [ 4] 15 A bag contains black and red balls. with at least two of each colour. Two balls are drawn from the bag without replacement. The number of red balls drawn is given by the random variable X. 2 (b) (i) Write down the probability of drawing two red balls. 15 (ii) Explain why the probability of drawing two black balls is ?. = P(X = o ) (iii) The bag contains a total of ten balls of which & are black. Find &. [5] 1 = 6 A game is played in which two balls are drawn from the bag of ten balls. without replace- ment. A player wins a prize if two black balls are drawn. (c) Olivia plays the game twelve times. Find the probability that she wins exactly three prizes. [2] 1 236 (d) William plays the game until he wins three prizes. Find the probability that he wins his third prize on his tenth attempt. 14] 0 :035 7 binomadt ( 12, - 2, 3 )