Question

two dice are tossed, 1 being red and the other blue. find the probability of a 3 on the red die or a 3 on the blue die or a 3 on both dice. select an answer 11/36 1/36 1/3 1/6

Explanation:

Step1: Calculate total outcomes

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

Step2: Calculate probability of 3 on red die

The probability of getting a 3 on the red die (blue - die can be any number) is $P(R = 3)=\frac{6}{36}$ (6 possibilities for the blue die).

Step3: Calculate probability of 3 on blue die

The probability of getting a 3 on the blue die (red - die can be any number) is $P(B = 3)=\frac{6}{36}$.

Step4: Calculate probability of 3 on both

The probability of getting a 3 on both dice is $P(R = 3,B = 3)=\frac{1}{36}$.

Step5: Use addition rule for probability

By the addition rule of probability $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, here $A$ is the event of 3 on red die and $B$ is the event of 3 on blue die. So $P((R = 3)\cup(B = 3))=\frac{6}{36}+\frac{6}{36}-\frac{1}{36}=\frac{6 + 6-1}{36}=\frac{11}{36}$.

Answer:

$\frac{11}{36}$