Question

A beach resort has 29 jet skis for guests to rent. Of these, 14 are two-person skis, 18 haveturbo packs, and 10 are both for two persons and have turbo packs. LetTbe the event that a jetski, randomly chosen, is a two-person ski, and letPbe the event that the ski has a turbo pack.A jet ski is chosen at random for rental. Find the probability for each of the following events.

Answer 1

Questions:

a. The jet ski is for two persons and has turbo packs.

b. The jet ski is not for two persons but has turbo packs.

Answer:

`P(P\ and\ T) = (10)/(29)`

`P(P\ and\ T') = (270)/(841)`

Explanation:

Given

`n=29` --- Total

`T = 14` --- Two person skis

`P = 18` --- Turbo packs skis

`P\ and\ T = 10` --- Two person ski and Turbo packs

Solving (a):

This is represented as:
`P(P\ and\ T)`

This is calculated as:

`P(P\ and\ T) = (n(P\ and\ T))/(n)`

`P(P\ and\ T) = (10)/(29)`

Solving (a):

This is represented as:
`P(P\ and\ T')`

This is calculated as:

`P(P\ and\ T') = P(P)\ and\ P(T')`

`P(P\ and\ T') = P(P)\ *\ P(T')`

Using the complement rule, we have:

`P(T') = 1 - P(T)`

The equation becomes:

`P(P\ and\ T') = P(P)\ *\ [1 - P(T)]`

`P(P\ and\ T') = (n(P))/(n)\ *\ [1 - (n(T))/(n)]`

`P(P\ and\ T') = (18)/(29)\ *\ [1 - (14)/(29)]`

`P(P\ and\ T') = (18)/(29)\ *\ (29-14)/(29)`

`P(P\ and\ T') = (18)/(29)\ *\ (15)/(29)`

`P(P\ and\ T') = (18*15)/(29*29)`

`P(P\ and\ T') = (270)/(841)`