An integer is chosen at random from 1 to 50. Find the probability that the number is

i) Divisible by 5

ii) A perfect cube

iii) A prime number

Solution:

Total number of outcomes = 50

i) Numbers divisible by 5 in 1 to 50 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Number of favourable outcomes = 10

Probability = Number of favourable outcomes/Total number of outcomes

The probability that the number is divisible by 5 = 10/50 

= 1/5

ii) Perfect cubes in 1 to 50 are 1, 8, and 27.

Number of favourable outcomes = 3

Probability = Number of favourable outcomes/Total number of outcomes

The probability that the number is a perfect cube = 3/50

iii) Prime numbers in 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

Number of favourable outcomes = 15

Probability = Number of favourable outcomes/Total number of outcomes

The probability that the number is a prime number = 15/50

= 3/10

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