Question

There are 9 black balls and 5 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that at least 3 black balls are drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Black balls = 9

Red balls = 5

Total balls = 14

Number of balls drawn = 4

Case 1: 3 Black balls & 1 Red ball drawn

Number of ways of drawing 4 balls from 14 balls is:

Number of ways of drawing 3 Back balls from 9 back balls is

Number of ways of drawing 1 Red ball from 5 Red balls is:

So,

P(3 Black balls) = 84 X 5/ 1001 = 0.4196

Case 2: 4 Black balls drawn

Number of ways of drawing 4 balls from 14 balls is:

Number of ways of drawing 4 Back balls from 9 back balls is

So,

P(4 Black balls) = 126/ 1001 = 0.1259

So,

P(At least 3 Black balls) = 0.4196 + 0.1259 = 0.5455

So,

Answer is:

0.5455