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  • Perplex
    IB Math AASL
    /
    Distributions & Random Variables
    /

    Problem Bank

    [Maximum mark: 7]

    Brett plays a game that costs ​$3​ per turn. Each turn, he spins a wheel with four numbered sections, and wins ​$X, where ​X​ is the section the wheel lands on. The probability distribution for ​X​ is shown in the following table, where ​p,q∈R.

    ​x​

    ​1​

    ​3​

    ​3p​​

    ​11​

    ​P(X=x)​

    ​60p​​

    ​q​

    ​10p​​

    ​0.1​

    1. Show that ​q=6054−7p​.

      [1]
    2. Hence find the possible value(s) of ​q​ such that the game is fair.

      [6]

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