## Exam-Style Question on Probability## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 562. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is not allowed.

A red spinner is designed with five possible outcomes. Let \(X\) be the score obtained when the spinner is spun. The probability distribution for \(X\) is given in the following table.

\(x\) | 3 | 4 | 5 | 8 | 10 |

\(P(X=x)\) | \(p\) | \(2p\) | \(p\) | \(2p\) | \(p\) |

(a) Find the value of p.

(b) Find the value of \(E(x)\).

A blue spinner is also designed with five possible outcomes. Let \(Y\) be the score obtained when the spinner is spun. The probability distribution for \(Y\) is given in the following table.

\(y\) | 1 | 2 | 3 | 4 | 5 |

\(P(Y=y)\) | \(r\) | \(r\) | \(q\) | \(q\) | \(q\) |

(c) State the range of possible values of \(q\).

(d) State the range of possible values of \(r\).

(e) Hence find the range of possible values of \(E(Y)\).

Arnold and Bernie play a game using these spinners. Arnold spins the red spinner once and Bernie spins the blue spinner once. The probability that Arnold's score is less than Bernie's score is \(\frac{1}{7}\).

(f) Find the value of \(E(Y)\).

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