# Exam-Style Questions on Probability Distribution

## Problems on Probability Distribution adapted from questions set in previous Mathematics exams.

### 1.

IB Standard

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 $$P(R \gt 2 )$$.

### 2.

IB Analysis and Approaches

Amelia selects a disc from a bag containing 5 green discs, 4 blue discs and 3 red discs.

She wins £1 for a green disc, £3 for a blue disc, and £7 for a red disk. The game costs £4 to play.

(a) Calculate the expected gain for this game, and hence show that the game is not fair.

After a while, $$n$$ red discs are added and Amelia wins £5 if she selects one. The game is now fair.

(b) Create an equation to represent this information.

(c) Hence, calculate the value of $$n$$.

### 3.

IB Applications and Interpretation

A game is played with a biased five-sided spinner. The possible scores, $$X$$ and their probabilities are shown in the following table.

 Score $$x$$ -5 -1 0 2 10 $$P(X=x)$$ 0.2 p 0.3 0.3 0.1

(a) Find the exact value of p.

Jaedee plays the game once.

(b) Calculate the expected score.

Jaedee plays the game twice and adds the two scores together.

(c) Find the probability Jaedee has a total score of 10.

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