Question

question 5 of 10
a video game randomly chooses your car color and type. the probability of getting a red car is 0.20, and the probability of getting a convertible is 0.40.
event a = you get a red car.
event b = you get a convertible.
a and b are independent events if

a. the probability of getting a red car or a convertible is 0.08.
b. the probability of getting a red convertible is 0.
c. the probability of getting a red car or a convertible is 0.60.
d. the probability of getting a red convertible is 0.08.

Explanation:

Step1: Recall the formula for independent events

For two independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\).

Step2: Calculate \(P(A)\times P(B)\)

Given \(P(A) = 0.20\) (probability of getting a red car) and \(P(B)=0.40\) (probability of getting a convertible). Then \(P(A)\times P(B)=0.20\times0.40 = 0.08\).

Step3: Interpret the result

If \(A\) and \(B\) are independent, the probability of both \(A\) and \(B\) occurring (getting a red convertible) is \(P(A\cap B)\), which should equal \(P(A)\times P(B) = 0.08\).

Answer:

C. The probability of getting a red convertible is 0.08.