Six people (of whom two are doctors) are waiting at a hospital for taxis to take

Question

Six people (of whom two are doctors) are waiting at a hospital for taxis to take them home. Three of the people are women, two of them being mothers. Two taxis arrive, and in a spirit of fairness two people are selected by simple random sampling to take the taxis. Select from the following list the correct probability for each of the events in questions 42 - 46. (a) 1/15 (b) 4/15 (c) 3/10 (d) 1/3 (e) 2/5 (f) 1/2 (g) 3/5 (h) 2/3 (i) 4/5 (j) cannot be determined from the information given. The taxis are taken by one person of each sex. The taxis are taken by one man and one mother. At least one of the mothers gets a taxi. Both doctors take the taxis. The taxis are taken by one mother and one doctor.

Explanation / Answer

We would be using combinations for this and the same can be calculated as below: -

42.

3C1*3C1/6C2=9/15=3/5=g

43.

3C1*2C1/6C2=6/15=2/5=e

44.

2C1*4C1/6C2+2C2*4C0/6C2=10/15=2/3=h

45.

2C2*4C0/6C2=1/15=a

46.

2C1*2C1/6C2=4/15=b

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