sparkle6 wrote: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
[spoiler]Answer: E. Can someone pleas explain using combination theory?[/spoiler]
First we need to recognize that the given information tells us that the 7 people consist of:
- a sibling trio
- a sibling pair
- and another sibling pair
Using counting techniques:
For this question, it's easier to find the complement.
So P(not siblings) = 1 -
P(they are siblings)
P(they are siblings) = [# of ways to select 2 siblings] / [total # of ways to select 2 people]
# of ways to select 2 siblings
Case a) 2 siblings from the sibling trio: from these 3 siblings, we can select 2 siblings in 3C2 ways (3 ways)
Case b) 2 siblings from first sibling pair: we can select 2 siblings in 2C2 ways (1 way)
Case c) 2 siblings from second sibling pair: we can select 2 siblings in 2C2 ways (1 way)
So, total number of ways to select 2 siblings = 3+1+1 = 5
total # of ways to select 2 people
We have 7 people and we want to select 2 of them
We can accomplish this in 7C2 ways (21 ways)
So,
P(they are siblings) =
5/21
This means P(
not siblings) = 1 -
5/21
= 16/21 =
E
Cheers,
Brent
