Question

Selena and Tracey play on a softball team.Selena has 8 hits out of 20 times at bat, andTracey has 6 hits out of 16 times at bat.Based on their past performance, what is theprobability that both girls will get a hit nexttime at bat?[A] 31 40[B] 48 320[C] 1 [D] 14 36

Answer 1

The correct option is option [B].

The probability that both girls Selena and Tracey will a next at bat is
`(48)/(320)`.

Explanation:

Independent events:

If A and B are event. The occurrence of one of them does not affect the outcomes of other event. Then A and B are independent events.

P(A and B) =P(A)× P(B)

Dependent events:

If A and B are event. The outcomes of one of them affects the outcomes of other event. Then A and B are called dependent events.

P(A and B) =P(A)× P(B|A)= P(B)×P(A|B)

Given that,

Selena has 8 hits out of 20 times at bat.

The number of hits by Tracey out of 16 is 6 at bat.

A= Selena hits a softball.

B= Tracey hits a softball.

The probability that the Selena his a softball is

=P(A)

`=(8)/(20)`

The probability that the Tracey his a softball is

=P(B)

`=(6)/(16)`

Both event are independent. Sine the events do not affect the outcomes of other event.

The probability that both girls will a next at bat is

=P(A and B)

=P(A)×P(B)

`=(8)/(20)* (6)/(16)`

`=(48)/(320)`