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

Question id: 396. This question is similar to one that appeared on an IB Standard paper in 2019. The use of a calculator is allowed.

A random variable \(R\) has the probability distribution as shown in the following table:

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

\(P(R=r)\) | 0.2 | a | b | 0.25 | 0.15 |

(a) Given that \(E(R) = 2.85\) find \(a\) and \(b\).

(b) Find \( P(R \gt 2 )\).

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