The tool shop has 8 power screw drivers and two have a short

The tool shop has 8 power screw drivers and two have a short. A foreman takes 4 of the screw drivers to his crew. That is the probability that fewer than two have a short?

Solution

P(fewer than 2 have a short) = 1 - P(2 have a short)

P(2 have a short and 2 dont have a short) = 2C2 * 6C2 / 8C4 = 3/14

P(fewer than 2 have a short) = 1 - 3/14

1 - 3/14

14/14 - 3/14

11/14 ---> ANSWER