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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.

Respuesta :

MrRoyal

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:

[tex]P(P\ and\ T) = \frac{10}{29}[/tex]

[tex]P(P\ and\ T') = \frac{270}{841}[/tex]

Step-by-step explanation:

Given

[tex]n=29[/tex] --- Total

[tex]T = 14[/tex] --- Two person skis

[tex]P = 18[/tex] --- Turbo packs skis

[tex]P\ and\ T = 10[/tex] --- Two person ski and Turbo packs

Solving (a):

This is represented as: [tex]P(P\ and\ T)[/tex]

This is calculated as:

[tex]P(P\ and\ T) = \frac{n(P\ and\ T)}{n}[/tex]

[tex]P(P\ and\ T) = \frac{10}{29}[/tex]

Solving (a):

This is represented as: [tex]P(P\ and\ T')[/tex]

This is calculated as:

[tex]P(P\ and\ T') = P(P)\ and\ P(T')[/tex]

[tex]P(P\ and\ T') = P(P)\ *\ P(T')[/tex]

Using the complement rule, we have:

[tex]P(T') = 1 - P(T)[/tex]

The equation becomes:

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

[tex]P(P\ and\ T') = \frac{n(P)}{n}\ *\ [1 - \frac{n(T)}{n}][/tex]

[tex]P(P\ and\ T') = \frac{18}{29}\ *\ [1 - \frac{14}{29}][/tex]

[tex]P(P\ and\ T') = \frac{18}{29}\ *\ \frac{29-14}{29}[/tex]

[tex]P(P\ and\ T') = \frac{18}{29}\ *\ \frac{15}{29}[/tex]

[tex]P(P\ and\ T') = \frac{18*15}{29*29}[/tex]

[tex]P(P\ and\ T') = \frac{270}{841}[/tex]