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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling a number greater than $5$ and then rolling a $6$ ? $\newline$ Simplify your answer and write it as a fraction or whole number. $\newline$ _____

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Probability of independent and dependent events

Full solution

Q. You roll a

6

-sided die two times.

\newline

What is the probability of rolling a number greater than

5

and then rolling a

6

?

\newline

Simplify your answer and write it as a fraction or whole number.

\newline

_____

Probability of Rolling > $5$ : The possible outcomes of rolling a $6$ -sided die are ${1, 2, 3, 4, 5, 6}$ . The probability of rolling a number greater than $5$ is P(\text{Rolling a number} > 5) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{6}
Probability of Rolling a $6$ : The possible outcomes of rolling a $6$ -sided die are ${1, 2, 3, 4, 5, 6}$ . The probability of rolling a $6$ is $P(\text{Rolling a 6}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{6}$
Probability of Rolling > $5$ and $6$ : We found that P(\text{Rolling a number} > 5): $\frac{1}{6}$ and $P(\text{Rolling a 6})$ : $\frac{1}{6}$ . The probability of rolling a number greater than $5$ and then rolling a $6$ is P(\text{Rolling a number} > 5) \times P(\text{Rolling a 6}) = $\frac{1}{6} \times \frac{1}{6}$ = $\frac{1}{36}$

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Question

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\newline

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\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

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\newline

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