Question

In a class activity all the 15 students wear hats. seven students wear red hats six students wear green hats two students wear white hats. two of the 15 students are picked at random show that the probability that these two students wear hats of the same color is 37/105

Answer 1

Explanation:

To find the probability that two students picked at random will wear hats of the same color, we can divide the number of successful outcomes by the total number of possible outcomes.

There are a total of 15 students, and we are picking two of them at random, so there are a total of 15 * 14 = 210 possible pairs of students.

There are 7 students wearing red hats, so there are 7 * 6 = 42 pairs of students who are both wearing red hats.

There are 6 students wearing green hats, so there are 6 * 5 = 30 pairs of students who are both wearing green hats.

There are 2 students wearing white hats, so there are 2 * 1 = 2 pairs of students who are both wearing white hats.

Altogether, there are 42 + 30 + 2 = 74 successful outcomes (pairs of students who are wearing hats of the same color).

The probability that two students picked at random will wear hats of the same color is therefore 74/210 = 37/105.