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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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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 $P(\text{Rolling a number} < 4) \times P(\text{Rolling a 3}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$

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college students running for student government class president. The candidates include

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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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Complete the statement. Round your answer to the nearest thousandth.

\newline

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