Question

At a peace summit, seven Hatfield and nine McCoy family

members sit down for a meeting. If the Sheriff orders two
randomly selected participants to shake hands at the end of
the meeting, what is the probability that the two are from
different families?

Answer 1

0.525 = 52.5% probability that the two are from different families.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, the order in which the two participants are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Desired outcomes:

1 from the Harfield family(from a set of 7).

1 from the McCoy family(from a set of 9). So

`D = C_(7,1)*C_(9,1) = (7!)/(1!6!)*(9!)/(1!8!) = 7*9 = 63`

Total outcomes:

2 from a set of 16. So

`T = C_(16,2) = (16!)/(2!14!) = 120`

Probability:

`p = (D)/(T) = (63)/(120) = 0.525`

0.525 = 52.5% probability that the two are from different families.