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

Answer:

$Probability = \frac{243}{1024}$

Step-by-step 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:

$p= \frac{1 + 2 + 6}{36}$

$p= \frac{9}{36}$

$p= \frac{1}{4}$

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

$q = 1 - p$ --- Complement rule

$q = 1 - \frac{1}{4}$

Take LCM

$q = \frac{4 - 1}{4}$

$q = \frac{3}{4}$

The probability of not getting audited in 5 rolls is:

$Probability = q^5$

$Probability = (\frac{3}{4})^5$

$Probability = \frac{3^5}{4^5}$

$Probability = \frac{243}{1024}$