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Sample Question 18:
Step 1: Acknowledge that there are 2 dice with 2 evens and 4 odds on each die.
Step 2: Understand that for the sum to be even, both dice rolls must show either 2 odds or 2 evens.
Step 3: Calculate the probability for rolling 2 odds. Since there are 4 odd numbers available on each dice roll, multiplying gives \(4 * 4 = 16\) total ways.
Step 4: Similarly, calculate ways to roll 2 evens. There are 2 even numbers available on each dice roll, and multiplying those gives \(2 * 2 = 4\).
Step 5: Calculate the total number of ways to roll an even sum by adding the ways to roll 2 odds and 2 evens. This gives a total of \(16 + 4 = 20\) ways.
Step 6: The total number of outcomes on a 2 dice roll is \(6 * 6 = 36\). So the probability of getting an even sum is \(\frac{20}{36} = \frac{5}{9}\). Thus the answer is \( (C) \frac{5}{9}\).
The faces of each of two fair dice are numbered 1, 2, 3, 5, 7, and 8. When the two dice are tossed, what is the probability that their sum will be an even number?
\(\textbf{(A) }\frac{4}{9}\qquad\textbf{(B) }\frac{1}{2}\qquad\textbf{(C) }\frac{5}{9}\qquad\textbf{(D) }\frac{3}{5}\qquad\textbf{(E) }\frac{2}{3}\)
Answer Keys
Question 18: CSolutions
Question 18Step 1: Acknowledge that there are 2 dice with 2 evens and 4 odds on each die.
Step 2: Understand that for the sum to be even, both dice rolls must show either 2 odds or 2 evens.
Step 3: Calculate the probability for rolling 2 odds. Since there are 4 odd numbers available on each dice roll, multiplying gives \(4 * 4 = 16\) total ways.
Step 4: Similarly, calculate ways to roll 2 evens. There are 2 even numbers available on each dice roll, and multiplying those gives \(2 * 2 = 4\).
Step 5: Calculate the total number of ways to roll an even sum by adding the ways to roll 2 odds and 2 evens. This gives a total of \(16 + 4 = 20\) ways.
Step 6: The total number of outcomes on a 2 dice roll is \(6 * 6 = 36\). So the probability of getting an even sum is \(\frac{20}{36} = \frac{5}{9}\). Thus the answer is \( (C) \frac{5}{9}\).