1. Sam and Angela decide to join a Dance club. The club includes 7 women and 7 men (including Sam and Angela). The club decides to select a woman and a man to lead the dance group. What is the probability that Sam and Angela will NOT be selected.
The Way to do this would be 1- 1/7* 1/7... But I wanted to ask that the ORDER is not important here and hence should the probab for them to be selected be 2/49 instead of 1/49.
2. What is the probab of selecting a woman and a man from a group of 7 women and 7 men.
Would this be 7C1 * 7C1/14C2 (As order does not matter here)
Basically what is the difference between the above two questions which makes the aproach different.
Two questions are altogether different.
In the first question you can select any male except Sam AND can select any female except Angela. Th egroup of two must have one male and one female.
Total cases = 7C1 * 7C1 = 49
How many cases when Sam and Angela are selected = 1
Prob of NOT selecting these two = 1-1/49 = 48/49
Second question is asking the probability of selecting a particular man and a particular woman out of 7 men and 7 women.
In how many ways you can select any man and any women = 7C1 * 7C1 = 49
Ways when a particular man and a particular woman are selected = 1
Prob = 1/49
If second question asks: What is the probabilty of selecting 2 people from 7 men and 7 women so that the group of 2 have 1 man and 1 woman then the answer is
Total cases = 14C2 = 91
Cases when both are men = 7C2 = 21
Cases when both are women = 7C2 = 21
Cases when one is man and one is woman = 91 -42 = 49
Prob = 49/91 or 7C1 * 7C1/14C2
Hope this helps.
SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008