Perplex
Dashboard
Topics
Exponents & LogarithmsApproximations & ErrorSequences & SeriesMatricesComplex NumbersFinancial Mathematics
Cartesian plane & linesFunction TheoryModellingTransformations & asymptotes
2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random VariablesInference & Hypotheses
DifferentiationIntegrationDifferential Equations
Review VideosFormula BookletMy Progress
BlogLanding Page
Sign UpLogin
Perplex
Perplex
Dashboard
Topics
Exponents & LogarithmsApproximations & ErrorSequences & SeriesMatricesComplex NumbersFinancial Mathematics
Cartesian plane & linesFunction TheoryModellingTransformations & asymptotes
2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random VariablesInference & Hypotheses
DifferentiationIntegrationDifferential Equations
Review VideosFormula BookletMy Progress
BlogLanding Page
Sign UpLogin
Perplex
IB Math AIHL
/
Probability
/
Problem Bank
IB Math AIHL
/
Probability
/
Problem Bank

Ask Plex AI about this problem

Get hints, ask questions, and work through this problem step by step

I'm Plex, here to help with problems on this worksheet!

Ask Plex AI about this problem

Get hints, ask questions, and work through this problem step by step

I'm Plex, here to help with problems on this worksheet!
[Maximum mark: 6]

Let ​R​ be the value of a roll on a ​6​-sided die. The probability distribution for ​R​ is shown in the following table.

​r​

​1​

​2​

​3​

​4​

​5​

​6​

​P(R=r)​

​0.1​

​0.1​

​p​

​q​

​0.2​

​0.2​

Sally rolls the die ​100​ times, and records ​25​ rolls of ​6.

  1. Explain why this is not inconsistent with the table.

    [1]

Josh plays a game using this die. He pays ​$4​ to roll the die, and earns back the value of his roll in dollars.

  1. Determine the value of ​p​ and the value of ​q​ such that the game is fair.

    [5]
[Maximum mark: 6]

Let ​R​ be the value of a roll on a ​6​-sided die. The probability distribution for ​R​ is shown in the following table.

​r​

​1​

​2​

​3​

​4​

​5​

​6​

​P(R=r)​

​0.1​

​0.1​

​p​

​q​

​0.2​

​0.2​

Sally rolls the die ​100​ times, and records ​25​ rolls of ​6.

  1. Explain why this is not inconsistent with the table.

    [1]

Josh plays a game using this die. He pays ​$4​ to roll the die, and earns back the value of his roll in dollars.

  1. Determine the value of ​p​ and the value of ​q​ such that the game is fair.

    [5]