Question

Consider a bin containing 1,000 balls numbered 1 to 1,000 where every ball numbered with an integer divisible by 10 is red and every other ball is blue. In the experiment where 10 balls are selected (without replacing the balls between selections) for which of the following pairs of events E1 and E2 is |E1 ∩ E2| != 0

Answer 1

|E1 ∩ E2| != 0

E1 and E2 are two events and we have to check if they are mutually exclusove or not

if they are mutually exclusive then : |E1 ∩ E2| = 0

and if they are not mutually exclusive then : |E1 ∩ E2| != 0

therefore for the condition to be met the events E1 and E2 must not be mutually exclusive

EXAMPLE :

E1 : there are exactly 2 red balls in the 10 balls picked

E2 : there is atleast 1 red ball in the 10 balls picked

they are not mutually exclusive as they will both occur when exactly 2 red balls are there

(please upvote)