Question

Event v occurs 28% of the time on Tuesdays.

and event v and event w occur together 19%
of the time on Tuesdays. Given that event v
occurs on a Tuesday, what is the probability
that event w occurs with event v?
A. 47%
B. 58%
C. 68%
D. 75%​

Answer 1

68%

Explanation:

Probability of occurrence of Event v = P(v) = 28% = 0.28

Probability of occurrence of both Events v and Event w together = P(v and w) = 19% = 0.19

We have to find what is the probability that event w occurs with event v given that event v occurs on a Tuesday. This is a conditional probability. In other words we have to find what is the probability of event w given that event v occurs of Tuesday. i.e we have to find P(w|v)

The formula to calculate this conditional probability is:

`P(w|v) = (P(v \cap w))/(P(v))`

Using the given values, we get:

`P(w|v) = (0.19)/(0.28)\\\\ P(w|v) = 0.68\\\\ P(w|v) = 68\%`

Therefore, the probability that even w will occur with event v given that event v occurs on Tuesday is 68%