An integer is chosen from 1 and 99. What is the probability that it is
1. Divisible by 3 and 5
2. Not divisible by 3 and 5
3. A perfect square
4. A prime number
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1. Divisible by 3 and 5 = 0.06
2. Not divisible by 3 and 5 = 0.94
3. A perfect square = 0.08
4. A prime number = 0.24
Solution:
The probability of event is given as:
An integer is chosen from 1 and 99
1. Divisible by 3 and 5
Favorable outcomes = 15, 30, 45, 60, 75, 90 = 6
Total number of outcomes = 1 to 99 = 100
Therefore,
2. Not divisible by 3 and 5
Number which are not divisible by 3 and 5 = 100 - 6 = 94
3. A perfect square
Favorable outcomes = perfect square = 4, 9, 16, 25, 36, 49, 64, 81
Favorable outcomes = 8
4. A prime number
Prime number between 1 and 99 are :
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 83, 89, 97 = 24
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