Transum Software

Exam-Style Questions on Probability Distribution

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


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


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 \(n\).


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.

If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.


Exam-Style Questions Main Page


Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.


Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2022 WWW.TRANSUM.ORG