Two integers are drawn at random from the set 5,6, . ., 35 . What is the probability that their difference is odd?

Step-by-step solution

Two integers are drawn from 5,6, , 35 Given, integer are 31 Total ways of choosing 2 integer from 31 integers = ³¹ C₂ Two integer difference will be odd only when one is even and other is odd. Let A be the event of selecting two integers whose difference is odd. Now, P(A)+P( A )=1P( A )= Probability of selecting two integers whose difference is not odd. Case I When two integers are even. Total ways of choosing 2 integer (even) from 15 even integers = ¹⁵ C₂ Case II When two integers are odd Total ways = ¹⁶ C₂ aligne