Question

Two unbiased dice are thrown simultaneously. Find the probability of getting a sum 5.

• A. 1/9
• B. 2/3
• C. 5/9
• D. 6/11

Hint:

The number of ways to get a sum $S$ on two dice (for $S \le 7$) is always $S - 1$.
Since $S = 5$, the number of favorable cases is $5 - 1 = 4$ out of 36, which immediately reduces to 1/9.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This probability question asks us to calculate the likelihood that rolling two standard six-sided dice simultaneously results in a face value sum of 5.

Step 2: Key Formula or Approach:
The formula for probability is:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]

Step 3: Detailed Explanation:
Let us evaluate the outcomes systematically:

• Calculate Total Outcomes:
Each die has 6 possible face values ($1, 2, 3, 4, 5, 6$).
For two dice, total possible outcomes $= 6 \times 6 = 36$ outcomes.

• Identify Favorable Outcomes:
We need the pairs of values $(x, y)$ such that $x + y = 5$:
- $(1, 4)$
- $(2, 3)$
- $(3, 2)$
- $(4, 1)$
There are no other combinations because a die face must be at least 1 and at most 6.
The number of favorable outcomes is exactly 4.

• Calculate Probability:
\[ P(\text{sum} = 5) = \frac{4}{36} = \frac{1}{9} \]

Step 4: Final Answer:
The probability of getting a sum of 5 is 1/9, which matches option (A).