Question

A red die is tossed and then a green dieis tossed. What is the probability thatthe red die shows an even number orthe green die shows an even number?Make sure your answer is reduced.3[?]Hint: The two events are not mutually exclusive. Soto the find the probability of the union, use:P(A or B) = P(A) + P(B) - P(A and B)L

Answer 1

Given:

A red die is tossed and then a green die is tossed.

Required:

We have to find the probability that the red die shows an even number or the green die shows an even number.

Explanation:

Let A denotes the event that the red die shows an even number and B denote the event that the green die shows an even number.

Here the total number of outcomes is 6(1-6) and the number of favorable outcomes are 3(2, 4, 6).

Then we have

$\begin{gathered} P(A)=\frac{3}{6}=\frac{1}{2} \\ \\ P(B)=\frac{3}{6}=\frac{1}{2} \end{gathered}$

Therefore,

$P(A\text{ and }B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$

Hence the probability that the red die shows an even number or the green die shows an even number is

$\begin{gathered} P(A\text{ or }B)=P(A)+P(B)+PA(A\text{ and }B) \\ \\ =\frac{1}{2}+\frac{1}{2}-\frac{1}{4} \end{gathered}$$\begin{gathered} =1-\frac{1}{4} \\ =\frac{3}{4} \end{gathered}$

Final answer: