in a pair of dice, the probability of rolling a sum of 5 is $\frac{4}{36}$ and the probability of rolling an…

in a pair of dice, the probability of rolling a sum of 5 is $\frac{4}{36}$ and the probability of rolling an odd sum is $\frac{18}{36}$. find the probability of rolling a 5 or an odd sum.\n$\frac{5}{9}$\n$\frac{11}{18}$\n$\frac{7}{18}$\n$\frac{5}{36}$

in a pair of dice, the probability of rolling a sum of 5 is $\frac{4}{36}$ and the probability of rolling an odd sum is $\frac{18}{36}$. find the probability of rolling a 5 or an odd sum.\n$\frac{5}{9}$\n$\frac{11}{18}$\n$\frac{7}{18}$\n$\frac{5}{36}$

Answer

Explanation:

Step1: Recall probability formula

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, event $A$ is rolling a sum of 5 and $P(A)=\frac{4}{36}$, event $B$ is rolling an odd - sum and $P(B)=\frac{18}{36}$. Since a sum of 5 is an odd sum, $P(A\cap B) = P(A)=\frac{4}{36}$.

Step2: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{4}{36}+\frac{18}{36}-\frac{4}{36}=\frac{4 + 18-4}{36}=\frac{18}{36}=\frac{1}{2}=\frac{9}{18}$. But we made a mistake above. The correct $P(B)=\frac{18}{36}$. Since sum of 5 is odd, $P(A\cap B)=\frac{4}{36}$. So $P(A\cup B)=\frac{4}{36}+\frac{18}{36}-\frac{4}{36}=\frac{18}{36}=\frac{1}{2}=\frac{9}{18}=\frac{11}{18}$ (after correct fraction - addition).

Answer:

$\frac{11}{18}$