A carnival card game gives the contestant a one in three probability of successfully choosing the right card and

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A carnival card game gives the contestant a one in three probability of successfully choosing the right card and thereby winning the game. If a contestant plays the game repeatedly, what is the minimum number of times that he must play the game so that the probability that he never loses is less than \(1\%?\)

A. \(3\)
B. \(4\)
C. \(5\)
D. \(6\)
E. \(7\)

OA D

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Through a bit of trial and error, you’ll see that (2/3)^6 drops below the threshold. So the answer is D. 6.

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For this carnival game, you have a 1/3 chance of winning each time. To find the minimum number of times you need to play so that the probability of never losing (always winning) is less than a certain value, you calculate the probability of winning each time and multiply it by itself until it’s less than that value. So, do the math and you’ll see that the answer is D. 6.