Question

4.2 theoretical probability. mutually exclusive/not mutually exclusive. two dice are rolled. what is the probability p(sum is 4)? $\frac{5}{9}$ $\frac{1}{2}$ $\frac{1}{9}$ $\frac{1}{12}$

Explanation:

Step1: Find total number of outcomes

When two dice are rolled, each die has 6 possible outcomes. So the total number of outcomes is $6\times6 = 36$ by the multiplication - principle.

Step2: Find number of favorable outcomes

The pairs of numbers on the two dice that sum to 4 are (1, 3), (2, 2), and (3, 1). So there are 3 favorable outcomes.

Step3: Calculate the probability

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(\text{sum is }4)=\frac{3}{36}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$