7.7.0: Exercises

Contemporary Mathematics · LibreTexts

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    From LibreTexts, under not declared, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    For the following exercises, find the probabilities of events with the given odds in favor.

    Exercise \(\PageIndex{1}\)

    \(9{:}4\)

    Exercise \(\PageIndex{2}\)

    \(2{:}3\)

    Exercise \(\PageIndex{3}\)

    \(2{:}3\)

    Exercise \(\PageIndex{4}\)

    \(5{:}4\)

    Exercise \(\PageIndex{5}\)

    \(1{:}50\)

    Exercise \(\PageIndex{6}\)

    \(7{:}5\)

    Exercise \(\PageIndex{7}\)

    \(1{:}7\)

    Exercise \(\PageIndex{8}\)

    \(10{:}9\)

    For the following exercises, find the probabilities of events with the given odds against.

    Exercise \(\PageIndex{9}\)

    \(1{:}8\)

    Exercise \(\PageIndex{10}\)

    \(2{:}3\)

    Exercise \(\PageIndex{11}\)

    \(3{:}2\)

    Exercise \(\PageIndex{12}\)

    \(5{:}4\)

    Exercise \(\PageIndex{13}\)

    \(1{:}50\)

    Exercise \(\PageIndex{14}\)

    \(7{:}5\)

    Exercise \(\PageIndex{15}\)

    \(1{:}7\)

    Exercise \(\PageIndex{16}\)

    \(10{:}9\)

    In the following exercises, find the odds in favor of events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1, also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5{:}2\) and \(3{:}8\) can be reduced to \(2.5{:}1\) and \(1{:}2.67\)).

    Exercise \(\PageIndex{17}\)

    \(\frac{2}{7}\)

    Exercise \(\PageIndex{18}\)

    \(\frac1217\)

    Exercise \(\PageIndex{19}\)

    \(\frac{8}{9}\)

    Exercise \(\PageIndex{20}\)

    \(\frac{3}{8}\)

    Exercise \(\PageIndex{21}\)

    \(\frac{9}25\)

    Exercise \(\PageIndex{22}\)

    \(\frac{6}{7}\)

    Exercise \(\PageIndex{23}\)

    \(\frac1013\)

    Exercise \(\PageIndex{24}\)

    \(\frac{8}15\)

    In the following exercises, find the odds against events with the given probabilities. Give your answer as a ratio of whole numbers. If neither of those two numbers is 1, also give an answer as a ratio involving both 1 and a number greater than or equal to 1 (for example, the odds \(5{:}2\) and \(3{:}8\) can be reduced to \(2.5{:}1\) and \(1{:}2.67\)).

    Exercise \(\PageIndex{25}\)

    \(\frac{2}{7}\)

    Exercise \(\PageIndex{26}\)

    \(\frac1217\)

    Exercise \(\PageIndex{27}\)

    \(\frac{8}{9}\)

    Exercise \(\PageIndex{28}\)

    \(\frac{3}{8}\)

    Exercise \(\PageIndex{29}\)

    \(\frac{9}25\)

    Exercise \(\PageIndex{30}\)

    \(\frac{6}{7}\)

    Exercise \(\PageIndex{31}\)

    \(\frac1013\)

    Exercise \(\PageIndex{32}\)

    \(\frac{8}15\)

    In the following exercises, you are drawing from a deck containing only these 10 cards:
    \({\text{A}} ♡\), \({\text{A}} ♠\), \({\text{A}} ♣\), \({\text{A}} \diamondsuit\), \({\text{K}} ♠\), \({\text{K}} ♣\), \(\text{Q} ♡\), \(\text{Q} ♠\), \({\text{J}} ♡\), \({\text{J}} ♠\).

    Exercise \(\PageIndex{33}\)

    Let \(E\) be the event “draw an ace.”

    1. What is the probability of \(E\)?
    2. What are the odds in favor of \(E\)?
    3. What are the odds against \(E\)?
    Exercise \(\PageIndex{34}\)

    Let \(F\) be the event “draw a \(\heartsuit\)”.

    1. What is the probability of \(F\)?
    2. What are the odds in favor of \(F\)?
    3. What are the odds against \(F\)?
    Exercise \(\PageIndex{35}\)

    Let \(T\) be the event “draw two \(\spadesuit\) (without replacement).”

    1. What is the probability of \(T\) ?
    2. What are the odds in favor of \(T\)?
    3. What are the odds against \(T\)?

    7.7.0: Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.