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You roll a $6$ -sided die two times. What is the probability of rolling a $6$ and then rolling a $6$ ? Write your answer as a fraction or whole number.

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Probability of independent and dependent events

Full solution

Q. You roll a

6

-sided die two times. What is the probability of rolling a

6

and then rolling a

6

? Write your answer as a fraction or whole number.

Calculate Probability of Rolling a $6$ : Determine the probability of rolling a $6$ on a single roll of a $6$ -sided die. Since there are $6$ sides on the die, and only one of those sides is a $6$ , the probability of rolling a $6$ on one roll is $1$ out of $6$ . Calculation: $P(\text{rolling a } 6) = \frac{1}{6}$
Calculate Probability of Rolling a $6$ Again: Determine the probability of rolling a $6$ on the second roll of the die. $\newline$ The probability of rolling a $6$ on the second roll is independent of the first roll, so it is also $1$ out of $6$ . $\newline$ Calculation: $P(\text{rolling a } 6 \text{ again}) = \frac{1}{6}$
Calculate Combined Probability: Calculate the combined probability of rolling a $6$ on the first roll and a $6$ on the second roll. $\newline$ Since the two events are independent, we multiply the probabilities of each event occurring. $\newline$ Calculation: $P(\text{rolling a } 6 \text{ and then a } 6) = P(\text{rolling a } 6 \text{ on first roll}) \times P(\text{rolling a } 6 \text{ on second roll}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$

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