Question

In a game called Taxation and Evasion, a player rolls a pair of dice. If, on any turn, the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she does not get audited is ________.

Answer 1

`Probability = (243)/(1024)`

Explanation:

Given

`Sum = \{7, 11, 12\}`

`Rolls = 5`

Required

Probability of not getting audited

If a pair of dice is rolled, the following are the observations of the sum

`Outcomes = 36`

`Sum\ of\ 7 = 6`

`Sum\ of\ 11 = 2`

`Sum\ of\ 12 = 1`

So, in a single roll; The probability of getting audited is:

`p= (1 + 2 + 6)/(36)`

`p= (9)/(36)`

`p= (1)/(4)`

The probability of not getting audited in a single roll is:

`q = 1 - p` --- Complement rule

`q = 1 - (1)/(4)`

Take LCM

`q = (4 - 1)/(4)`

`q = (3)/(4)`

The probability of not getting audited in 5 rolls is:

`Probability = q^5`

`Probability = ((3)/(4))^5`

`Probability = (3^5)/(4^5)`

`Probability = (243)/(1024)`