An integer is chosen between 70 and 100. Find the probability that it is a prime number.

A
$\frac{5}{29}$
B
$\frac{6}{29}$
C
$\frac{1}{2}$
D
$\frac{3}{2}$

Solution:

Given that, an integer is chosen between 70 and 100.
We know that,
Required probability =

\frac{Number of favorable outcomes}{Total number of outcomes}

.
So, integers between 70 and 100 are {71, 72, 73, 74,75 ……..,98, 99}.
Total Number of possible outcomes = 29.
Now, prime numbers between 70 and 100 are {71, 73, 79, 83, 89, 97}.
Therefore, number of favorable outcomes = 6.
Let E = Event of getting the prime numbers between 70 and 100.
Substitute the given values in the formula,
Required probability =