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Perplex
IB Math AASL
/
Distributions & Random Variables
/
Problem Bank
IB Math AASL
/
Distributions & Random Variables
/
Problem Bank

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[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]