Question

Probability of getting sum 7 or 9 when two dice are thrown is:

• A. \(\frac{5}{18}\)
• B. \(\frac{1}{6}\)
• C. \(\frac{1}{9}\)
• D. None of these

Hint:

Always count ordered pairs for dice problems.

Answer 1

The Correct Option is A

To calculate the probability of getting a sum of 7 or 9 when two dice are thrown, we need to consider the possible outcomes for each die. Each die has 6 faces, so there are a total of \( 6 \times 6 = 36 \) possible outcomes when two dice are thrown.

Now, let's find the number of favorable outcomes for each case:

1. Sum of 7: The combinations of dice rolls that result in a sum of 7 are:
   
   • (1, 6)
   • (2, 5)
   • (3, 4)
   • (4, 3)
   • (5, 2)
   • (6, 1)
2. Sum of 9: The combinations of dice rolls that result in a sum of 9 are:
   
   • (3, 6)
   • (4, 5)
   • (5, 4)
   • (6, 3)

In total, the number of favorable outcomes is \( 6 + 4 = 10 \).

The probability of getting a sum of 7 or 9 is given by the formula:

\(\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}}\)

Thus, the probability is:

\(\frac{10}{36} = \frac{5}{18}\)

Therefore, the correct answer is \(\frac{5}{18}\).