Question

A bag contains n counters. one counter is blue and the rest are red. Two counters are taken at random from the bag. a) express, in terms of n, the probability that a counter of each colour is taken. Give your answer as a fraction. b) the probability that a counter of each colour is taken is 0.125. How many red counters are in the bag?

Answer 1

A] Probability = 1/n ; B] Number = 8

Explanation:

Total counters = n , Blue counter = 1 , Red counters (remaining) = n -1

A] Prob (One blue, & One red counter) = (Blue counter / Total counters) x (Red counters / Total remaining counters) = [1 / n] x [ (n -1) / (n-1)] = 1 / n

Alternative, Prob (One red, & one blue) = (Red counter / Total counters) x (Blue counters / remaining counters) = [ (n-1) / n ] x [1 / (n-1) ] = 1 / n

B] Prob (each color , a blue & red counter taken) = 0.125 {Given}

By A], this Prob = 1/n.

So, 0.125 = 1/n → n = 1 / 0.125 = 8