Question

Freshman Sophomore Junior Senior Left-handed batters 4 6 5 4 Right-handed batters 13 10 11 12 A school baseball team has 65 players. What is the probability that a randomly chosen player is a junior or a right-handed batter? A) 11/65 B) 14/65 C) 16/65 D) 51/65

Answer 1

Answer: D)
`(51)/(65)`

Explanation:

The given table is :

Freshman Sophomore Junior Senior

Left-handed batters 4 6 5 4

Right-handed batters 13 10 11 12

From the table, the number of player that are junior =
`5+11=16`

The probability of choosing a junior=
`P(J)=(16)/(65)`

The number of players that are right- handed =
`13+10+11+12=46`

The probability of choosing right handed batter=
`P(R)=(46)/(65)`

The probability of choosing a junior and a right handed batter

`P(J\cap R)=(11)/(65)`

Now, the number of player that are junior or a right-handed batter is given by :-

`P(J\cap R)=P(J)+P(R)-P(J\cap R)\\\\\Rightarrow P(J\cap R)=(16)/(65)+(46)/(65)-(11)/(65)\\\\\Rightarrow P(J\cap R)=(51)/(65)`