A jar contains 20 red, 20 blue, 6 yellow and 4 pink balls. If two balls are to be selected at random and without replacement, approximately what is the probability both of them to be the same colour?  Pick:
A) 1 / 25  B) 1 / 15  C) 1 / 3  D) 1 / 2  E) 1

Rationale: ok so jar contains 20 red 20 blue 6 yellow and 4 pink . . adding the number of balls we get 50 total . . now its a counting + probability exercise . . 2 stages exist : pick first ball then second ball . . denominator for first ball = 50 since there are 50 balls denominator for second ball = 49 since only 49 would remain for each type ball i constructed probability of getting 2 of same . . i used a counting method . . first ball 20 chances blue and 2 nd ball 19 chances blue and so on and so forth blue = ( 20 * 19 ) / ( 50 * 49 ) rounded to 400 / 2500 red = ( 20 * 19 ) / ( 50 * 49 ) rounded to 400 / 2500 yellow = ( 6 * 5 ) / ( 50 * 49 ) rounded to 30 / 2500 pink = ( 4 * 3 ) / ( 49 * 50 ) rounded to 12 / 2500 then i summed these individual probabilities to get 842 / 2500 this is ~ 1 / 3 as 800 * 3 = 2400 ans : c
Answer: C