## On Auditorium Riddles To Solve

## Solving On Auditorium Riddles

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## The Prime Number Riddle

Two hundred people in an auditorium are asked to think of a single digit number from 1 to 9 inclusive and write it down. All those who wrote down a prime number are now asked to leave. Ninety people remain behind in the hall. How many of these are expected to have written down an odd number?

Hint: Remember that 1 is not a prime number.

Those that remain behind must have written {1,4,6,8,9} and from this only {1,9} are odd. The probability of an odd number is thus 2/5.

Expected number of odds is 2/5 * 90 = 36

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Expected number of odds is 2/5 * 90 = 36

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