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5-32.

Assume that two standard dice are being rolled. Let event $\text{A} = \text{{the sum is a multiple of 3}}$ and $\text{event B} = \text{{the sum is a multiple of 4}}$. The $P(A)=\frac{12}{36}$ and the $P(B)=\frac{9}{36}$. Homework Help ✎

1. How many outcomes are in the intersection of events $\text{A and B}$?

Make a table or grid with all the sum possibilities for two rolled die,
i.e. $1+1=2$, $1+2=3$, etc.
How many outcomes are multiples of both $3$ and $4$?

2. What is $P(\text{A or B})$?

Use the table or list you created for part (a).

Remember to exclude all outcomes that apply to both events.
$P(\text{A or B})=P(\text{A})+P(\text{B})-P(\text{A and B})$

$P(\text{A or B})=\frac{20}{36}$