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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling an even number and then rolling an even number? $\newline$ 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 an even number and then rolling an even number?

\newline

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

\newline

_____

Identify Total Outcomes: Identify the total number of outcomes for one roll of a $6$ -sided die. $\newline$ Since a $6$ -sided die has $6$ faces, there are $6$ possible outcomes for each roll.
Identify Favorable Outcomes: Identify the number of favorable outcomes for rolling an even number on a $6$ -sided die. $\newline$ The even numbers on a $6$ -sided die are $2$ , $4$ , and $6$ . Therefore, there are $3$ favorable outcomes for rolling an even number.
Calculate Probability of Even Number: Calculate the probability of rolling an even number on one roll of a $6$ -sided die. $\newline$ The probability of rolling an even number on one roll is the number of favorable outcomes divided by the total number of outcomes. $\newline$ Probability of rolling an even number = Number of favorable outcomes / Total number of outcomes = $\frac{3}{6} = \frac{1}{2}$
Calculate Probability of Two Rolls: Since the die rolls are independent events, calculate the probability of rolling an even number twice in a row. $\newline$ The probability of two independent events both occurring is the product of their individual probabilities. $\newline$ Probability of rolling an even number twice = $(1 / 2) \times (1 / 2) = 1 / 4$

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\text{[B]Raffle B}

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Question

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\newline

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\newline

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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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