There are three different types of circus prizes marked big (B), medium (M) and

Question

There are three different types of circus prizes marked big (B), medium (M) and little (L). Each contains a certain number of red (R) and gold (G) balls, distributed as follows big prize (B) :6R and 5G medium prize (M): 4R and 2G little prize (L) 1R and 1G Your friend wins 3 big prizes,1 medium prize and 2 little prizes. Without looking, you randomly reach into one of her prizes, and randomly take out one of its balls, which happens to be gold (G). Calculate the probability that you were choosing from a little prize bag. PUG) = Number

Explanation / Answer

To Find P(L/G) = P(L) * P(G/L)/ P(G)

P(L) = 2/6 = 1/3 (Total 6 prizs of which 2 are little)

P(G/L) = Probability of getting a gold given that it comes from a little prize).

Each little Prize has 1 R and 1 G. Total 2 balls of which 1 is red. Therefore P(G/L) = 1/2

P(G) = P(Big prize) * P(getting a gold given its a Big Prize) + P(Medium prize) * P(getting a gold given its a medium Prize) + P(Small prize) * P(getting a gold given its a small Prize)

P(G) = P(B) * P(G/B) + P(M) * P(G/M) + P(L) * P(G/L)

P(B) = 3/6 = 1/2

P(G/B) = 5/11

P(M) = 1/6

P(G/M) = 2/6 = 1/3

Therefore P(G) = (1/2 * 5/11) + (1/6 * 1/3) + (1/3 * 1/2) = 5/22 + 1/18 + 1/6 = 89/198

Therefore P(L/G) = (1/3) * (1/2)/ (89/198) = 33/89 = 0.3708

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