If you roll two fair six-sided dice, what is the probability that the sum is $4$ or higher?

View step-by-step help

Home

Math Problems

Algebra 1

Outcomes of compound events

Full solution

Q. If you roll two fair six-sided dice, what is the probability that the sum is

4

or higher?

Calculate Total Outcomes: question_prompt: What's the probability that the sum of two rolled dice is $4$ or more?
Find Outcomes Less Than $4$ : Calculate the total number of possible outcomes for rolling two dice. Since each die has $6$ faces, the total outcomes are $6 \times 6$ .
Subtract Outcomes: Total outcomes = $6 \times 6 = 36$ .
Calculate Favorable Outcomes: Now, find the number of outcomes where the sum is less than $4$ . These are $(1,1)$ , $(1,2)$ , and $(2,1)$ .
Calculate Probability: Number of outcomes where the sum is less than $4 = 3$ .
Simplify Fraction: To get the number of outcomes where the sum is $4$ or more, subtract the outcomes where the sum is less than $4$ from the total outcomes.
Simplify Fraction: To get the number of outcomes where the sum is $4$ or more, subtract the outcomes where the sum is less than $4$ from the total outcomes. Number of favorable outcomes = Total outcomes - Outcomes where sum is less than $4$ .
Simplify Fraction: To get the number of outcomes where the sum is $4$ or more, subtract the outcomes where the sum is less than $4$ from the total outcomes. Number of favorable outcomes $=$ Total outcomes $-$ Outcomes where sum is less than $4$ . Number of favorable outcomes $= 36 - 3 = 33$ .
Simplify Fraction: To get the number of outcomes where the sum is $4$ or more, subtract the outcomes where the sum is less than $4$ from the total outcomes. Number of favorable outcomes $=$ Total outcomes $-$ Outcomes where sum is less than $4$ . Number of favorable outcomes $= 36 - 3 = 33$ . Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes.
Simplify Fraction: To get the number of outcomes where the sum is $4$ or more, subtract the outcomes where the sum is less than $4$ from the total outcomes. Number of favorable outcomes $=$ Total outcomes $-$ Outcomes where sum is less than $4$ . Number of favorable outcomes $= 36 - 3 = 33$ . Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. Probability $=$ Number of favorable outcomes $/$ Total outcomes.
Simplify Fraction: To get the number of outcomes where the sum is $4$ or more, subtract the outcomes where the sum is less than $4$ from the total outcomes. Number of favorable outcomes = Total outcomes - Outcomes where sum is less than $4$ . Number of favorable outcomes = $36 - 3 = 33$ . Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. Probability = Number of favorable outcomes / Total outcomes. Probability = $\frac{33}{36}$ .
Simplify Fraction: To get the number of outcomes where the sum is $4$ or more, subtract the outcomes where the sum is less than $4$ from the total outcomes. Number of favorable outcomes = Total outcomes - Outcomes where sum is less than $4$ . Number of favorable outcomes = $36 - 3 = 33$ . Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. Probability = Number of favorable outcomes / Total outcomes. Probability = $\frac{33}{36}$ . Simplify the fraction to get the final probability.
Simplify Fraction: To get the number of outcomes where the sum is $4$ or more, subtract the outcomes where the sum is less than $4$ from the total outcomes. Number of favorable outcomes $=$ Total outcomes $-$ Outcomes where sum is less than $4$ . Number of favorable outcomes $= 36 - 3 = 33$ . Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. Probability $=$ Number of favorable outcomes $/$ Total outcomes. Probability $= 33 / 36$ . Simplify the fraction to get the final probability. Probability $= 11 / 12$ .