Question

two 6 - sided dice are rolled at the same time. how many outcomes correspond to the event that the sum of the numbers is 5?
a. 2
b. 3
c. 4
d. 5

Explanation:

Step1: Define possible pairs

Let the outcomes of the two dice be \( (x, y) \), where \( x \) is the result of the first die and \( y \) is the result of the second die. We need \( x + y = 5 \), and \( 1\leq x\leq6 \), \( 1\leq y\leq6 \).

Step2: Find valid pairs

Solve for \( x \) and \( y \):

• If \( x = 1 \), then \( y = 5 - 1 = 4 \) (so \( (1, 4) \))
• If \( x = 2 \), then \( y = 5 - 2 = 3 \) (so \( (2, 3) \))
• If \( x = 3 \), then \( y = 5 - 3 = 2 \) (so \( (3, 2) \))
• If \( x = 4 \), then \( y = 5 - 4 = 1 \) (so \( (4, 1) \))
• For \( x = 5 \), \( y = 0 \) (invalid, since die can't show 0)
• For \( x = 6 \), \( y = -1 \) (invalid)

So the valid pairs are \( (1, 4) \), \( (2, 3) \), \( (3, 2) \), \( (4, 1) \). Count them: 4 outcomes.

Answer:

C. 4