5) Two bags are given. Bag one (Bi) contains 10 Red and 5 Blue balls. Bag two (B

Question

5) Two bags are given. Bag one (Bi) contains 10 Red and 5 Blue balls. Bag two (B2) contains 4 Red and 8 Blue balls. a) Four balls are drawn without replacement from Bag one. Find the probability that they are all Red. b) Four balls are selected from Bag two with replacement. Find the probability that two are Red and the other two Blue. a) A bag is selected at random and a bal is drawn from it at random i) Find the probability that the ball is Blue. ii Given that the ball is Blue, find the probability that t came from B

Explanation / Answer

a)
4 balls from 15 balls can be selected in 15C4 ways
4 red balls from 10 red balls can be selected in 10C4 ways

Required probability = 10C4/15C4 = 0.1846

b)
4 balls from 12 balls can be seleced in 12C4 ways
2 red balls from 4 red balls can be selected in 4C2 ways and 2 blue balls from 8 blue balls can be selected in 8C2 ways

required probability = 4C2*8C2/12C4 = 0.3394

c)
i)
P(Blue) = P(B1)*P(Blue) + P(B2)*P(Blue)
= 1/2*1/15 + 1/2*8/12
= 0.3667

ii)
P(B1|Blue) = P(Blue|B1)*P(B1)/P(Blue)
= (1/2*1/15)/(1/2*1/15 + 1/2*8/12)
= 0.0909

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