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

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.

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Trúc Chi 4 years 2021-09-04T13:47:56+00:00 1 Answers 11 views 0

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  1. Bo
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    2021-09-04T13:49:10+00:00
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    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) = \frac{10}{29}

    P(P\ and\ T') = \frac{270}{841}

    Step-by-step 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) = \frac{n(P\ and\ T)}{n}

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

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

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

    P(P\ and\ T') = \frac{18}{29}\ *\ \frac{15}{29}

    P(P\ and\ T') = \frac{18*15}{29*29}

    P(P\ and\ T') = \frac{270}{841}

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