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You roll a $6$ -sided die two times. What is the probability of rolling a number greater than \(3\) and then rolling a number less than \(4\)? Write your answer as a percentage. ____ `%`

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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 number greater than \(3\) and then rolling a number less than \(4\)? Write your answer as a percentage. ____ `%`

Find Probability of > $3$ : First, let's find the probability of rolling a number greater than $3$ . That's rolling a $4$ , $5$ , or $6$ . So, $3$ out of $6$ numbers work. $\newline$ $P(>3) = \frac{3}{6} = \frac{1}{2}$ .
Find Probability of $<4$ : Next, we need the probability of rolling a number less than $4$ , which is rolling a $1$ , $2$ , or $3$ . Again, $3$ out of $6$ numbers work. $\newline$ $P(<4) = \frac{3}{6} = \frac{1}{2}.$
Multiply Probabilities: Now, we multiply the two probabilities together to get the combined probability. So, it's $\frac{1}{2}$ times $\frac{1}{2}$ . $\newline$ $P(>3 \text{ and then } <4) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}.$
Convert to Percentage: Finally, we convert the fraction to a percentage. Multiply $\frac{1}{4}$ by $100$ to get the percentage. $\newline$ $(\frac{1}{4}) \times 100\% = 25\%.$

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