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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling a number greater than $3$ and then rolling a number greater than $3$ ? $\newline$ Write your answer as a percentage. $\newline$ $\_\_\_\_\_$ %

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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

3

and then rolling a number greater than

3

?

\newline

Write your answer as a percentage.

\newline

\_\_\_\_\_

%

Die Probability Calculation: The possible outcomes of rolling a die are $\{1, 2, 3, 4, 5, 6\}$ . The probability of rolling a number greater than $3$ is $P(\text{Rolling a number} > 3) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}$
Independent Events Probability: Since the two rolls are independent events, the probability of rolling a number greater than $3$ on the first roll and then again on the second roll is the product of the two individual probabilities. $\newline$ $P(\text{Rolling a number} > 3 \text{ and then} > 3) = P(\text{Rolling a number} > 3) \times P(\text{Rolling a number} > 3)$ $\newline$ $= \frac{1}{2} \times \frac{1}{2}$ $\newline$ $= \frac{1}{4}$
Percentage Conversion: The probability is $1 / 4$ . To write the probability as a percentage, multiply the probability by $100$ . $\newline$ $(1 / 4 \times 100)\% = 25\%$

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