Question

two dice are tossed, 1 being red and the other blue. find the probability of a 4 on the red die or a 4 on the blue die or a 4 on both dice.

Explanation:

Step1: Calculate total outcomes

When two dice are tossed, the total number of outcomes is $6\times6 = 36$ since each die has 6 faces.

Step2: Calculate number of favorable outcomes

The number of outcomes with a 4 on the red - die: The red die shows 4 and the blue die can show any of the 6 values, so there are 6 outcomes.
The number of outcomes with a 4 on the blue - die: The blue die shows 4 and the red die can show any of the 6 values, so there are 6 outcomes. But we have double - counted the outcome (4, 4) once.
The number of favorable outcomes is $6 + 6-1=11$.

Step3: Calculate probability

The probability $P$ is the number of favorable outcomes divided by the total number of outcomes. So $P=\frac{11}{36}$.

Answer:

$\frac{11}{36}$