A THREE DIGIT NUMBER IS SELECTED AT RANDOM. WHAT IS THE PROBABILITY THAT NONE OF THE THREE DIGITS ARE PRIME.

IF POSSIBLE PLEASE HELP THANK YOU

Glenn

Hi Glenn,

To form a three digit number you can use any of the nine digits from 1 to 9 as the first digit and then any of the ten digits from 0 to 9 as the second and third digits. Thus there are 9x10x10 = 900 three digit numbers.

Of the ten digits, 6 are not prime. They are

0, 1, 4, 6, 8 and 9 To form a three digit number from 0, 1, 4, 6, 8 and 9 you can use any of the five digits from {1, 4, 6, 8, 9} as the first digit and then any of the six digits from {0, 1, 4, 6, 8, 9} as the second and third digits. Thus there are 5x6x6 = 180 three digit numbers.

Hence if you select a three digit number at random the probability that none of its digits are prime is

 180/900 =  1/5

Cheers,
Harley
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