Alice\'s cooler contains 13 lemonades and 5 Sprites. Bob\'s cooler contains 3 le

Question

Alice's cooler contains 13 lemonades and 5 Sprites. Bob's cooler contains 3 lemonades and 8 Sprites. Unfortunately, the two coolers look identical, making them indistinguishable from the outside. (a) Suppose Bob selects a cooler at random and then chooses a drink at random. What is the probability it is a lemonade? (b) Suppose that the drink he chose was indeed a lemonade. What is the probability he is choosing from his own cooler? (c) Now suppose he pulls out two more drinks, both of which are lemonades. In other words, he has drawn three lemonades in a row. Now what is the probability he is choosing from his own cooler?

Explanation / Answer

A) P(lemonade) = 0.5 x 13/18 + 0.5 x 3/11

= 0.4975

B) P(lemonade | his own cooler) = p(lemonade from his own cooler)/0.4975

= (0.5x3/11)/0.4975

= 0.2741

C) P(3 lemonades from alice's cooler) = 13C3/18C3 = 0.35

P(3 lemonades from his own cooler) = 3C3/11C3 = 0.006

P(chosing from own cooler) = 0.006/(0.35 + 0.006) = 0.017

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