Question

The probability that Ashley drives faster than the speed limit (event A) is 0.34, and the probability that he gets a speeding ticket (event B) is 0.22. The probability that he drives faster than the speed limit, given that he has gotten a speeding ticket, is 1. Are events A and B dependent or independent? A. dependent B. independent C. insufficient data D. depends on the other events in the sample space

Answer 1

The correct answer between all

the choices given is the first choice or letter A. I am hoping that this answer

Answer 2

Answer: Option 'A' is correct

Explanation:

Since we have given that

A be the event that Ashley drives faster than the speed limit.

P(A)=0.34

B be the event that he gets a speeding ticket.

P(B)=0.22

Probability that he drives faster than the speed limit, given that he has gotten a speeding ticket i.e.

P(A|B)=1

but for A and B to be independent ,

P(A).P(B)= P(A and B)

0.34×0.22=0.0748

but,

`P(A\mid B)=(P(A\cap B))/(P(B))\\\\1=(P(A\cap B))/(0.22)\\\\0.22=P(A\cap B)`

So, P(A∩B) does not satisfy the condition.

Hence, A and B are not independent events.

Option 'A' is correct as they are dependent events.