A salesperson is selling eight types of genie lamps, made of gold, silver, brass

Question

A salesperson is selling eight types of genie lamps, made of gold, silver, brass or iron and purportedly containing male or female genies. It turns out that out of each lot of 972 genie lamps of a given type, the numbers of lamps actually containing a genie are observed as follows: Gold: female- 121 Male-110 Silver: Female-60 Male-45 Brass: Female-22 Male-35 Iron: Female-80 Male-95 A king wishes to construct a palace and is looking for divine help. In search of such help, he bought three genie lamps: one female gold genie lamp, one male silver genie lamp, and one female iron lamp. A) What is the probability that a genie will appear from all three lamps? B) What is the probability exactly one genie will appear? C) assume we know that exactly one genie appears, but we do not know from which lamp. What is the conditional probability that a female genie appears?

Explanation / Answer

These are independent distributions

1) Hence, Probability = 121/972*(45/972)*(80/972) = 0.000475

2) There are 3 cases possible :

Required probability = P( female gold + P(male silver) + P(iron female) =

(121/972)*(1-45/972)*(1-80/972) + (1-121/972)*(1-45/972)*(80/972) + (1-121/972)*(45/972)*(1-80/972) = 0.214

3) Required probability from Bayess theorem as

[P( Female gold ) + P(Female iron)] / [ P( female gold + P(male silver) + P(iron gold) ] = [(121/972)*(1-45/972)*(1-80/972) + (1-121/972)*(1-45/972)*(80/972) ] /0.214 = 0.8302

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