Question

A survey of 46 college athletes found that 24 played volleyball, while 22 played basketball. a) If we pick one athlete survey participant at random, what is the probability they play basketbali? b) If we pick 2 athletes at random (without replacement), what is the probability we get one volleyball player and one basketball player?

Answer 1

A)
`(11)/(23)`

B)
`(88)/(345)`

Explanation:

A survey of 46 college athletes found that

• 24 played volleyball,
• 22 played basketball.

A) If we pick one athlete survey participant at random, the probability they play basketball is

`P_1=(22)/(46)=(11)/(23)`

B) If we pick 2 athletes at random (without replacement),

• the probability we get one volleyball player is
  `(24)/(46)=(12)/(23);`
• the probability we get another basketball player is
  `(22)/(45)` (only 45 athletes left).

Thus, the probability we get one volleyball player and one basketball player is

`P_2=(12)/(23)\cdot (22)/(45)=(88)/(345)`