Each two-digit number is written on a paper slip and these are all pu

1.	Each two-digit number is written on a paper slip and these are all put in a box. What is the probability that the product of the digits of a number drawn is a prime number? What if three-digit numbers are used instead?
Answer» Total two-digit numbers = 90 Product of the digits of a number drawn is a prime number 12, 13, 15, 17, 21, 31, 51, 71. (1 is not a prime number) Total number whose product of the digits drawn is a prime number = 8 Probability of product of the digits drawn is a prime number = \(\frac{8}{90}=\frac{4}{45}\) Total three-digit numbers = 900 Product of the digits of a number drawn is a prime number 112, 113, 115, 117, 121, 131, 151, 171, 211, 311, 511, 711. Total number whose product of the digits drawn is a prime number = 12 Probability of product of the digits drawn is a prime number = \(\frac{12}{900}=\frac{4}{300} =\frac{1}{75}\)

Each two-digit number is written on a paper slip and these are all put in a box. What is the probability that the product of the digits of a number drawn is a prime number? What if three-digit numbers are used instead?

Answer»

Total two-digit numbers = 90

Product of the digits of a number drawn is a prime number 12, 13, 15, 17, 21, 31, 51, 71.

(1 is not a prime number)

Total number whose product of the digits drawn is a prime number = 8

Probability of product of the digits drawn is a prime number = \(\frac{8}{90}=\frac{4}{45}\)

Total three-digit numbers = 900

Product of the digits of a number drawn is a prime number 112, 113, 115, 117, 121, 131, 151, 171, 211, 311, 511, 711.

Total number whose product of the digits drawn is a prime number = 12

Probability of product of the digits drawn is a prime number = \(\frac{12}{900}=\frac{4}{300} =\frac{1}{75}\)

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