Question

4. A middle school chess club has 3 members: Adam, Dave, and Carol. Two students from the club will be selected at random to participate in the county chess tournament. What is the probability that a boy and a girl will be selected?

Answer 1

`1`

Explanation:

There are 3 total students in the club, so there are 3 possible first students that could be selected. After the first student is selected, there are 2 remaining students to choose from.

Since there are
`2` boys and
`1` girl in the club, the probability that a boy is selected as the first student is
`2/3`. The probability that a girl is selected as the second student, given that a boy was selected as the first student, is
`1/2`. Therefore, the probability of selecting a boy and a girl in that order is
`(2/3) * (1/2) = 1/3.`

The same is true if the order is reversed, so the probability of selecting a girl and a boy is also
`1/3`. Thus, the probability of selecting a boy and a girl in any order is
`2/3 + 1/3 = 1`.

In summary, the probability of selecting a boy and a girl at random from the club is
`1`.

Answer 2

boy probability 6

girl probability 1/6

Explanation:

There are 3 students in the chess club, 2 of whom are boys (Adam and Dave) and 1 of whom is a girl (Carol). There are 3 ways to choose the first student (Adam, Dave, or Carol) and 2 ways to choose the second student (Adam or Dave if the first student was Carol, or Carol if the first student was Adam or Dave). This means there are a total of 3*2=6 possible combinations of students who could be selected. Out of these 6 combinations, only 1 involves a boy and a girl (Adam and Carol). Therefore, the probability that a boy and a girl will be selected is 1/6.