Question

In a simultanous throw of two dice what is the probability of getting a total of 7?

• A. 1/6
• B. 1/8
• C. 1/9
• D. 1/12

Hint:

For two dice, the sum of 7 is the most frequent outcome because it has the highest number of combinations (6 out of 36). Keep this peak of the probability distribution in mind for quick calculations.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Probability measures the likelihood of a specific event occurring.
It is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space.
Key Formula or Approach:
The classical probability of an event $E$ is defined by: \[ P(E) = \frac{n(E)}{n(S)} \] where:
- $n(E)$ is the number of favorable outcomes.
- $n(S)$ is the total number of outcomes in the sample space.

Step 2: Detailed Explanation:
When two standard six-sided dice are rolled simultaneously:
- Each die has 6 possible outcomes (numbers 1 to 6).
- The size of the sample space $S$ is: \[ n(S) = 6 \times 6 = 36 \] Let $E$ be the event of rolling a total sum of 7.
Let's find all pairs of numbers $(d_1, d_2)$ from the two dice such that $d_1 + d_2 = 7$:
- If the first die shows 1, the second must show 6: $(1, 6)$
- If the first die shows 2, the second must show 5: $(2, 5)$
- If the first die shows 3, the second must show 4: $(3, 4)$
- If the first die shows 4, the second must show 3: $(4, 3)$
- If the first die shows 5, the second must show 2: $(5, 2)$
- If the first die shows 6, the second must show 1: $(6, 1)$
Thus, the set of favorable outcomes is: \[ E = \{(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)\} \] The total count of favorable outcomes is: \[ n(E) = 6 \] Now, calculate the probability: \[ P(E) = \frac{6}{36} = \frac{1}{6} \]

Step 3: Final Answer:
The probability of getting a total of 7 when rolling two dice is 1/6.