6. [10) Alex and Billie frequently go to restaurants together. Alex orders a sal
ID: 3306018 • Letter: 6
Question
6. [10) Alex and Billie frequently go to restaurants together. Alex orders a salad wi probability 0.5 and Billie orders a salad with probability 0.7 lie frequently go to restaurants together. Alex orders a salad with (i) Suppose that Alex and Billie order their meals independently. Determine the probability that exactly one of them will order a salad. (ii) Suppose Alex and Billie do not order their meals independently Ales w probab order a salad with probability 0.6 if Bilie orders a salad. Compute the of Billie ordering a salad if Alex orders one.Explanation / Answer
(i) The probability that Bill orders salad and Alex does not = 0.5 * (1 - 0.7)
= 0.5 * 0.3 = 0.15
Probability that Alex orders salad and Bill does not = 0.7 * (1 - 0.5)
= 0.7 * 0.3 = 0.21
=> Probability that exactly one orders salad = 0.15 + 0.21 = 0.36
(ii) P(Alex|Bill) = 0.6
Using Baye's theorem P(Alex Bill) = P(Alex|Bill) * P(Bill)
= 0.6 * 0.7 = 0.42
Using Baye's theorem P(Bill|Alex) = P(Alex Bill) /* P(Alex)
= 0.42 / 0.5
= 0.84
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