My SAMMYI A Chicago wine company wanting to promote their new wine has inserted

Question

My SAMMYI A Chicago wine company wanting to promote their new wine has inserted special corks in the bottles. Once a bottle of wine has been opened, one can view the bottom of the cork which will display one of three images of Sammy Sosa at bat, 20% of the new corks display Sammy preparing to bat, 30% of the new corks display Sammy swinging at a ball, and 50% display Sammy's bat breaking. As a life-long Sammy fan, you want to collect all 3 special corks. On average how many bottles of Chicago wine would you have to buy to obtain the 3 special corks? 0 A B

Explanation / Answer

Here we will calculate how many chichago wine bottle we have to buy to obain all 3 special corks.

Expected number of bottle needed = 1/ Pr(Sammy preparing to bat) + 1/ Pr(sammy sosa swinging at ball) + 1/ Pr(sammy bat breaking)

= 1/0.5 + 1/0.2 + 1/0.3 = 10.33

so it requires 10.33 bottles to buy to obtain all 3 special corks.

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