Question

A bag contains 15 counters: 7 red, 4 blue, and 4 green. A counter is taken out of the bag

at random. What is the probability of choosing the following:
a. a green counter?
b. a yellow counter?
c. a red or blue counter?

Answer 1

a. The probability of choosing a green counter is 4/15.

b. The probability of choosing a yellow counter is 0 since there are no yellow counters in the bag.

c. The probability of choosing a red counter is 7/15.

The probability of choosing a blue counter is 8/15.

The total number of counters in the bag can be found by solving for x in the equation (7/x) * (7/15) + ((x-7)/x) * (8/15) = 2 * (4/15).

This simplifies to x^2 - 22x + 105 = 0, which has solutions x = 15 and x = 7.

Since there are more blue counters than red counters, the total number of counters must be greater than or equal to 11, so the answer is that there are 15 counters in the bag.