In a lottery 50 tickets are sold in which 14 are of the prize. A man bought 2 tickets, then what is the probability that the man wins the prize?

To solve this problem, we need to use the concept of combinations in probability.

Step 1: Calculate the total number of ways to draw 2 tickets from 50. This is given by the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of tickets (50), r is the number of tickets drawn (2), and '!' denotes factorial.

So, the total number of ways to draw 2 tickets from 50 is C(50, 2) = 50! / [2!(50-2)!] = 1225.

Step 2: Calculate the number of ways to draw 2 tickets that are both prizes from the 14 prize tickets. This is given by C(14, 2) = 14! / [2!(14-2)!] = 91.

Step 3: The probability that the man wins the prize is given by the number of favorable outcomes (drawing 2 prize tickets) divided by the total number of outcomes (drawing any 2 tickets).

So, the probability = 91 / 1225 = 0.07428571428571429.

Therefore, the probability that the man wins the prize is approximately 0.074 or 7.4%.