A warehouse employs 22 workers on first shift and 14 workers

A warehouse employs 22 workers on first shift and 14 workers on second shift. Eight workers are chosen at random to be interviewed about the work enviroment.

A) find the probability of choosing all first-shift workers.

b) find the probability of choosing all second-shift workers.

c) find the probability of choosing exactly six first shift workers.

d) find the probability of choosing exactly four second-shift workers.

please provide how to calculate the problem so I understand it.

Thank you

Solution

Total number of workers = 22+14 = 36

Number of workers in first shift = 22

Number of workers in second shift = 14

a)

Favourable number of ways will consist of choosing all 8 workers from the 22 of the first shift workers.

Thus favourable number of ways = C(22,8)

Total number of ways = C(36,8)

Probability = C(22,8)/C(36,8) = 0.0106

b)

Favourable number of ways will consist of choosing all 8 workers from the 14 of the second shift workers.

Thus favourable number of ways = C(14,8)

Total number of ways = C(36,8)

Probability = C(14,8)/C(36,8) = 0.0001

c)

Favourable number of ways will consist of choosing 6 workers from the 22 of the first shift workers and 2 workers out of 14 second shift workers

Thus favourable number of ways = C(22,6)*C(14,2)

Total number of ways = C(36,8)

Probability = (C(22,6)C(14,2))/C(36,8) = 0.2244

d)

Favourable number of ways will consist of choosing 4 workers from the 22 of the first shift workers and 4 workers out of 14 second shift workers

Thus favourable number of ways = C(22,4)*C(14,4)

Total number of ways = C(36,8)

Probability = (C(22,4)*C(14,4))/C(36,8) = 0.2420