Bunuel wrote:
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
Kudos for a correct solution.
MANHATTAN GMAT OFFICIAL SOLUTION:This problem tests primarily on
Probability theory. In addition,
Exponents are needed to represent the impact of playing multiple games on the probability of the outcomes. The probabilities are given in fractions, yet the question is asked in terms of percents, so
FDP Connections are relevant.
Finally, the question is phrased in terms of an inequality, so
Inequalities come into play. However, all the secondary issues can be resolved relatively easily. Therefore, we can consider this question a minor hybrid problem, in which one of the content areas (probability) is much more important than the others.
“The probability that he never loses” can be rephrased as “the probability that he always wins.” This probability can be expressed as (1/3)^n, where 1/3 is the chance of winning on a single play and n is the number of times the contestant plays.
Let's track it in a chart:
![](https://gmatclub.com/forum/download/file.php?id=27041)
We might also have noticed that only the denominator in the probabilities mattered, as the numerator was always 1. To have a probability of less than 1%, the fractional probability must be “1 over something greater than 100.” In order for 3^n >100, n must be at least 5.
The correct answer is C.Attachment:
2015-06-22_1804.png [ 42.34 KiB | Viewed 7889 times ]