Question

5. Five bowls are labeled 1 - 5. Bowl j contains j white and 5-j red balls. Example: Bowl 2 contains 2 white and 3 red balls. One bowl is selected at random and two balls are selected (without replacement).

(a) What is the probability both balls are white?

(b) What is the probability both balls are red?

(c) What is the probability one ball is red and one ball is white?

(d) Write out the probability distribution for the number of white balls?

(e) What is the expected number of white balls selected.

(f) Let X be the random variable for the number of white balls selected. Find the E(X2 ).

Answer 1

© PCB;) = » j=1,2,3,4,5, Bi šW6-PR @ Pl both white): Plate PCB) to (0+ 4+ 3+ 6+10): 250 = 12/5 ⓇP (both oed) 3, 003) = [Vs] © P(1 ved, I white): Ž Bore: = sollx4+ 2x3+ 3x2+4x) = 20 = 275 @ of x be no of white balls, P(x=0) = Pl both red) = 5, P(x-1)=P(1W, IR) P(x = 2) = P(both while)- mere a © ECX) = 5xP(x) = 0 x Š + x + 2x = 102] ECYZ) = 5x2P(x) = 0 x B +2x = 12-01 GU OU