Question

In a realtor office, there are a total of 25 realtors. In that office, exactly 10 of the realtors visited every continent in the world. If someone were to fairly randomly pick 2 of the realtors, what is the probability that they will pick realtors that visited every continent in the world?

Answer 1

The probability of picking two realtors who have visited every continent is 3/20 or 0.15 (or 15%).

Explanation:

To calculate the probability, we need to consider the total number of ways to choose two realtors out of 25 and the number of ways to choose two realtors who have visited every continent.

The total number of ways to choose two realtors out of 25 can be calculated using combination notation (nCr):

Total ways = 25C2 = (25!)/(2!(25-2)!) = 300

Now, let's calculate the number of ways to choose two realtors who have visited every continent. Since there are exactly 10 realtors who have visited every continent, the number of ways to choose two of them can be calculated using combination notation:

Ways to choose 2 realtors who visited every continent = 10C2 = (10!)/(2!(10-2)!) = 45

Therefore, the probability of picking two realtors who have visited every continent is:

P = (Ways to choose 2 realtors who visited every continent) / (Total ways to choose 2 realtors)

P = 45/300

Simplifying this fraction, we get:

P = 3/20