Question

A box contains seven red balls and five black balls. Three balls are selected at random from the box. Compute the probability that (d) at least one ball is red.

Answer 1

From the question:

A box contains seven red balls and five black balls.

Three balls are selected at random from the box.

Formula:

Probability that at least 1 ball drawn is red = 1 - Probability that none of the 3 balls drawn are red

Probability that none of the 3 balls drawn are red =  (5c₃) / (12c₃)

Apply the formula: nC_r = n! / ((n−r)! * r!)

5c₃ = 5! / ((5−3)! * 3!) =10

12c₃ = 12! / ((12−3)! * 3!) =220

Probability that none of the 3 balls drawn are red = 10 / 220 = 1/22

Probability that at least 1 ball drawn is red = 1 - (1/22) = 21 / 22

Therefore the Probability that at least 1 ball drawn is red 21 / 22.