Question

In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?

A. 5/21 B. 3/7 C. 4/7 D. 5/7 E. 16/21

Answer 1

Option E

`(16)/(21)`

Explanation:

Number of ways of selecting two people from a group of seven people is

`C^2_(7)`

`(7 * 6* 5!)/(2*1* 5!) \\= 21`

Number of ways by which two people selected in a room come out to be siblings are -

`C^2_(2)`+
`C^2_(3)`+
`C^2_(2)`

`= (2*1)/(2*1) + (3*2*1)/(2*1) + (2*1)/(2*1)\\= 1+ 3+1\\= 5`

Number of ways by which two people selected in a room are not siblings

`= 1-`Probability of selecting two siblings

`= 1-(5)/(21) \\= (16)/(21)`

Hence, option E is correct