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Two dice are rolled. What is the probability of rolling a 3 and a 2?

Two dice are rolled. What is the probability of rolling a $3$ and a $2$ ?

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Compound events: find the number of outcomes

Full solution

Q. Two dice are rolled. What is the probability of rolling a

3

and a

2

?

Determine Total Outcomes: First, we need to determine the total number of possible outcomes when two dice are rolled. Since each die has $6$ faces, and each face is equally likely to come up, there are $6$ possible outcomes for the first die and $6$ possible outcomes for the second die. To find the total number of outcomes for two dice, we multiply the number of outcomes for one die by the number of outcomes for the other die. $\newline$ Calculation: $6 \times 6 = 36$
Identify Specific Rolls: Next, we need to identify the number of ways to roll a $3$ on one die and a $2$ on the other die. Since the dice are distinct, there are two different outcomes that satisfy this condition: rolling a $3$ on the first die and a $2$ on the second die, or rolling a $2$ on the first die and a $3$ on the second die. $\newline$ Calculation: There are $2$ favorable outcomes.
Calculate Probability: Now, we calculate the probability of rolling a $3$ and a $2$ . The probability is the number of favorable outcomes divided by the total number of possible outcomes. $\newline$ Calculation: Probability = Number of favorable outcomes / Total number of possible outcomes = $\frac{2}{36}$
Simplify Fraction: Finally, we simplify the fraction to its lowest terms to express the probability in simplest form. $\newline$ Calculation: $2 / 36$ can be simplified by dividing both the numerator and the denominator by $2$ . $\newline$ $2 / 36 = 1 / 18$

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