Question

12 employees are randomly selected from an engineering department. 10 are men and 2 are women. two employees are randomly selected from the sample with NO replacement between the draws.

A) Draw a tree diagram and label all branches and probabilities.

B) Whats the prob. that there will be at least one woman

C) prob. of no women.

D) prob. of 2 women.

E) prob. exactly one man and one woman.

Answer 1

As we are drawin 2 people without replacement from the sample of 10 men and 2 women, therefore the tree diagram here would be given as:

b) Probability of at least one woman

= 1 - Probability that both are men

= 1 - (10/12)*(9/11)

= 0.3182

Therefore 0.3182 is the required probability here.

c) Probability of no women

= 1 - Probability of at least one woman

= 1 - 0.3182

= 0.6818

Therefore 0.6818 is the required probability here.

d) Probability of 2 women

= (2/12)*(1/11)

= 0.0152

Therefore 0.0152 is the required probability here.

e) Probability of one man and one woman

= 2*(2)*(10)/12*11

= 0.3030

Therefore 0.3030 is the required probability here.