Question

In a professional gathering of engineers, the probability that a randomly chosen person is from the civil, mechanical, or electrical engineer is 0.10, 0.28, and 0.62 respectively.

a) If a group of 10 people is chatting, what is the probability that there are 3 mechanical and at least 6 electrical engineers?

b) What is the probability that you need to meet at least 6 engineers to meet 3 mechanical engineers?

Answer 1

P(civil) = 0.10,
P(mechanical) = 0.28
P(electrical) = 0.62

a) Probability  that there are 3 mechanical and at least 6 electrical engineers is computed here as:

= P(3 mechanical, 6 electrical and 1 civil) + P(3 mechanical and 7 electrical)

Therefore 0.1975 is the required probability here.

b) Probability that we need to meet at least 6 engineers to meet 3 mechanical engineers is computed as the probability of meeting less than 3 mechanical engineers in first 5 engineers met. This is computed using the binomial probability function as:

Therefore 0.8624 is the required probability here.