Two dice are thrown and their sum is noted.
Find the probability that:
© the sum is odd and greater than 8 .

Question

Two dice are thrown and their sum is noted. Find the probability that: (c) the sum is odd and greater than 8 .

UpStudy AI · Accepted Answer

1. The sample space when two dice are thrown has $$6 \times 6 = 36$$ equally likely outcomes.

2. We need the probability that the sum is odd and greater than 8. The possible sums that are both odd and greater than 8 are $$9$$ and $$11$$.

3. For a sum of $$9$$, the possible outcomes are:
   - $$(3, 6)$$
   - $$(4, 5)$$
   - $$(5, 4)$$
   - $$(6, 3)$$

This gives $$4$$ outcomes.

4. For a sum of $$11$$, the possible outcomes are:
   - $$(5, 6)$$
   - $$(6, 5)$$

This gives $$2$$ outcomes.

5. Therefore, the total number of favorable outcomes is:
   $$
   4 + 2 = 6
   $$

6. The probability $$P$$ is given by the ratio of favorable outcomes to total outcomes:
   $$
   P = \frac{6}{36} = \frac{1}{6}
   $$

Thus, the required probability is $$\frac{1}{6}$$.
The probability that the sum of two dice is odd and greater than 8 is $$\frac{1}{6}$$.

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