i have one algebra question. please give me a correct answer There are three dif

Question

i have one algebra question. please give me a correct answer

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 6G medium prize (M): 3R and 3G little prize (L): 2R 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 big prize bag. P{B|G) = Note: your answer should be entered with at least 2 significant figures.

Explanation / Answer

we will use Baye's theorem
P(B|G) = P (G|B)*P(B) / P(G)

P (G|B)*P(B) = 6/12 * 1/3
= 1/6

P(G)= P(B) * P(G|B) + P(M) * P(G|M) + P(L) * P(G|L)
= 1/3 * 6/12 + 1/3 * 3/6 + 1/3 * 1/3
= 1/6 + 1/6 + 1/9
= (3+3+2)/18
=8/18
= 4/9

P(B|G) = P (G|B)*P(B) / P(G)
= (1/6) / (4/9)
= (1/6)* (9/4)
= 3/8
Answer: 3/8 = 0.375

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