Cards bearing numbers 12, 13, 14, ... , 70, 71 (one number on one card) are kept in a box and then a card is drawn from the box without looking into it. What is the probability that the card drawn has the number which is not a prime ?

Correct Option: $\frac{3}{4}$

Step-by-Step Explanation:

Step 1: Determine the total number of possible outcomes.
The cards are numbered continuously from 12 to 71.
To find the total number of cards (total possible outcomes, $n\left(S\right)$):

$n\left(S\right)=71-12+1=60$

So, there are 60 cards in total.

Step 2: Find the prime numbers in the given range.
Let us list all the prime numbers strictly between 12 and 71 inclusive:
13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

Counting these prime numbers gives:

$\text{Total prime numbers}=15$

Step 3: Find the number of non-prime numbers.
We want the probability of drawing a card with a number that is not a prime.
The number of non-prime cards (favorable outcomes, $n\left(E\right)$) is:

$n\left(E\right)=\text{Total cards}-\text{Total prime numbers}$

$n\left(E\right)=60-15=45$

Step 4: Calculate the required probability.
The probability $P\left(E\right)$ of drawing a card that is not a prime number is given by:

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{45}{60}$

Simplifying the fraction by dividing both the numerator and the denominator by 15:

$P\left(E\right)=\frac{3}{4}$

Thus, the probability that the card drawn has a number which is not a prime is $\frac{3}{4}$.