Math, asked by babitharoshan0039, 10 months ago

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

Answers

Answered by sharonr
0

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:

Probability = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}

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,

Probability = \frac{6}{100} = 0.06

2. Not divisible by 3 and 5

Number which are not divisible by 3 and 5 = 100 - 6 = 94

Probability = \frac{94}{100} = 0.94

3. A perfect square

Favorable outcomes = perfect square =  4, 9, 16, 25, 36, 49, 64, 81

Favorable outcomes = 8

Probability = \frac{8}{100} = 0.08

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

Probability = \frac{24}{100} = 0.24

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