You roll a 6-sided die two times. What is the probability of rolling a number less than 4 and then rolling a 3? Simplify your answer and write it as a fraction or whole number. _____

Probability of Number < 4: The possible outcomes of rolling a 6-sided die are {1, 2, 3, 4, 5, 6}. The probability of rolling a number less than 4 (which includes 1, 2, or 3) is P(Rolling a number < 4) = Favorable outcomes / Total outcomes = 3 / 6 = 1 / 2Probability of Rolling a 3: Next, we need to find the probability of rolling a 3. Since there is only one outcome that is a 3, the probability is P(Rolling a 3) = Favorable outcomes / Total outcomes = 1 / 6Combined Probability of Events: Now, we need to find the combined probability of both events happening in sequence. This is found by multiplying the probabilities of each individual event. So, the probability of rolling a number less than 4 and then rolling a 3 is P(Rolling a number < 4) * P(Rolling a 3) = 1 / 2 * 1 / 6 = 1 / 12

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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling a number less than $4$ and then rolling a $3$ ? $\newline$ Simplify your answer and write it as a fraction or whole number. $\newline$ _____

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Math Problems

Algebra 1

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 less than

4

and then rolling a

3

\newline

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

\newline

_____

Probability of Number < $4$ : The possible outcomes of rolling a $6$ -sided die are $\{1, 2, 3, 4, 5, 6\}$ . The probability of rolling a number less than $4$ (which includes $1$ , $2$ , or $3$ ) is P(\text{Rolling a number} < 4) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
Probability of Rolling a $3$ : Next, we need to find the probability of rolling a $3$ . Since there is only one outcome that is a $3$ , the probability is $P(\text{Rolling a 3}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{6}$
Combined Probability of Events: Now, we need to find the combined probability of both events happening in sequence. This is found by multiplying the probabilities of each individual event. So, the probability of rolling a number less than $4$ and then rolling a $3$ is P(\text{Rolling a number} < 4) \times P(\text{Rolling a 3}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}