Pelin's problematic calculator (from University Entrance Examination in Turkey 2017 LYS-1)

Probability Level 3

Pelin's calculator has only a broken "3" key.

Whenever this key is pressed, the calculator calculates it as 3, 4, and 6 with 1/6, 1/3, and 1/2 probabilities, respectively.

Pelin wants to calculate "23 - (12/3)" with this calculator.

Accordingly, what is the probability that Pelin will find the result of "23 - (12/3)" as 22?

1/4 5/12 7/24 1/3 1/9

G Gürsoy by G Gürsoy , 36, Turkey

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1 solution

Joshua Lowrance
Aug 16, 2018

There are two ways that the calculator can read 22: 26 - (12/3) or 24 - (12/6).

  1. There is a 1/2 chance that the 6 will show up in 26, and a 1/6 chance that the 3 will show up in (12/3). So the probability is 1/2 * 1/6 = 1/12
  2. There is a 1/3 chance that the 4 will show up in 24, and a 1/2 chance that the 6 will show up in (12/6). So the probability is 1/3 * 1/2 = 1/6

1/12 + 1/6 = 3/12 or 1/4

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