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Slugger at Bat

Slugger McCoy has a batting average of 0.333, which represents the likelihood that Slugger will get a hit when he is up at bat.

We know that in today's game, Slugger expects to be up to bat three times. What is the probability that Slugger will hit safely at least once?

 

Source: Adapted from Israel Rose's Algebra: An Introduction to Finite Mathematics, 1963, p. 341


Hint: The answer is not 1...i.e. Prob(head) = .5 does not mean that on every 2 flips of a coin, a "head" will appear.

Can you draw a tree diagram to represent the situation?

 


Solution Commentary: We know Prob(hit) = 1 - Prob(no hit) = 1 - (2/3)3 = 1 - (8/27) = 19/27 = 0.7037