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Alexus [3.1K]
3 years ago
13

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 ________.
Mathematics
1 answer:
AnnZ [28]3 years ago
7 0

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}

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