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Question

In a lottery of 50 tickets numbered 1 to 50, two tickets are drawn simultaneously. The probability that both the tickets are drawn have prime numbers is ?


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Solution

Step 1: Find the probability of getting a prime number in the first draw

Given: In a lottery of 50 tickets numbered 1 to 50, two tickets are drawn simultaneously.

We know that the number of prime numbers between 1 to 50 is 152,3,5,7,11,13,17,19,23,29,31,37,41,43,47.

Probability is given as

Probability=NumberoffavourableoutcomesNumberoftotaloutcomes

So, the probability of getting a prime number in the first draw will be=Totalprimenumberbetween1to50Totalnumberoftickets

=1550

Step 2: Find the probability of getting a prime number in the second draw

If 1 card is taken from the pack of lottery tickets, then the number of remaining prime numbers are 14.

The number of remaining lottery tickets =49

So, the probability of getting a prime number in the second draw will be=RemainingprimenumbersRemaningnumberoftickets

=1449

Therefore,

Step 3: Find the combined probability of getting 2 prime numbers in 2 draws

the probability of getting prime numbers in both draws= (The probability of getting a prime number in the first draw) ×(The probability of getting a prime number in the second draw )

=1550×1449=2102450=335

Hence, the probability that both the tickets are drawn have prime numbers is 335.


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