I tried to solve the problem by making all the sums as sample space and then counting for the sums that were odd and less than 8. I know the formula for the conditional probability but I am not sure of how to apply it there.
2026-04-05 14:47:52.1775400472
Suppose two dice are thrown and the sum of both numbers is observed is odd. Determine the probability that the sum is less than 8.
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We have the formula for conditional probability $$P(A|B)=\frac{P(A\cap B)}{P(B)}.$$
In this case, assign $A$ as "sum less than $8$" and $B$ as "sum is odd". As such, we have $P(A\cap B)=\frac13$ and $P(B)=\frac12$. Therefore, the answer is $\frac23$.