Question

quiz 6.4.1 - adding probabilities
this quiz will test your knowledge on when and how to add probabilities together.
value: 3
there are ten shirts in your closet, three blue, four green, and three red. you randomly select one to wear. what is the probability that it is blue or green?
○ a. 7/10
○ b. 3/25
○ c. 7/20
○ d. 3/5

Explanation:

Step1: Calculate probability of blue shirt

The probability of selecting a blue shirt $P(B)$ is the number of blue shirts divided by the total number of shirts. There are 3 blue shirts and 10 total shirts, so $P(B)=\frac{3}{10}$.

Step2: Calculate probability of green shirt

The probability of selecting a green shirt $P(G)$ is the number of green shirts divided by the total number of shirts. There are 4 green shirts and 10 total shirts, so $P(G)=\frac{4}{10}$.

Step3: Calculate probability of blue or green

Since the events of selecting a blue - shirt and a green - shirt are mutually exclusive, the probability of selecting a blue or green shirt $P(B\cup G)$ is $P(B)+P(G)$. So $P(B\cup G)=\frac{3}{10}+\frac{4}{10}=\frac{3 + 4}{10}=\frac{7}{10}$.

Answer:

A. 7/10