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If you roll two fair six-sided dice, what is the probability that the dice show the same number?

If you roll two fair six-sided dice, what is the probability that the dice show the same number?

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Outcomes of compound events

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Q. If you roll two fair six-sided dice, what is the probability that the dice show the same number?

Calculate Total Outcomes: First, figure out how many total outcomes there are for rolling two dice. Each die has $6$ sides, so $6$ outcomes per die. $\newline$ Calculate $6 \times 6$ for the total outcomes. $\newline$ $6 \times 6 = 36$
Find Matching Outcomes: Now, find the number of outcomes where both dice show the same number. There's $1$ way for each number to match ( $1$ - $1$ , $2$ - $2$ , ..., $6$ - $6$ ). $\newline$ Count these outcomes: $1$ , $2$ , $3$ , $1$ $0$ , $1$ $1$ , $6$ . That's $6$ outcomes where both dice match.
Calculate Probability: To get the probability, divide the number of matching outcomes by the total number of outcomes. $\newline$ Calculate $\frac{6}{36}$ to get the probability. $\newline$ $\frac{6}{36} = \frac{1}{6}$

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