Question

Consider two events such that P(A) =3/5 equals start fraction three over five end fraction , P(B) = 2/3 start fraction two over three end fraction , and P(A ∩ B) = 1/5 start fraction one over five end fraction . Are events A and B independent events?

Answer 1

\[P(A) = \frac{ 3 }{ 5 }\]
\[P(B) = \frac{ 2 }{ 3 }\]
And they say that:
\[P(A∩B) = \frac{ 1 }{ 5 }\]
But when we calculate the probabilities we get:
\[\frac{ 3 }{ 5 } \times \frac{ 2 }{ 3 } = \frac{ 6 }{ 15 } = \frac{ 2 }{ 5 }\]

Answer 2

thank u

Answer 3

Keep in mind that P(A∩B) is the probability of both events A and B happening (also written as the intersection of A and B).

Answer 4

So if we take the probabilities of both events and the probability is different than what they're saying it is, then it is not independent.