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?

Answer 1

The events A and B are both dependent. So, the answer to this question is (A) dependent.

Answer 2

Answer: They are not independent i.e. they are dependent.

Explanation:

Let A be the events that Ashley drives faster than the speed limit.

Let B be the events that Ashley gets a speeding ticket.

P(A) = 0.34

P(B) = 0.22

So, P(A) . P(B) = 0.34 × 0.22 = 0.0748

Since we have given that Probability that he drives faster than the speed limit given that he has gotten a speeding ticket i.e. P(A|B)=1

so, we will use "conditional probability":

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

since P(A∩B ) = 0.22 ≠P(A).P(B)=0.0748

Hence, they are not independent i.e. they are dependent.