Question

The compound probability of two events, E and F 1/8 , is ; the probability of E is 1/2 and of F is 1/3 . In two or more complete sentences, explain why E and F are not independent.

Answer 1

If they are independent then it should hold true that P(A) X P(B) = P(A and B)
This is not the case for F and E in the questions so therefore they are independent.

Answer 2

Event E and event F are not independent because:

`P(E\bigcap F)\\eq P(E)* P(F)`

Explanation:

We know that two event A and event B are said to be independent if:

P(A∩B)=P(A)×P(B)

Here we have two events as E and F such that:

`P(E\bigcap F)=(1)/(8)`

`P(E)=(1)/(2)`

and
`P(F)=(1)/(3)`

This means that:

`P(E)* P(F)=(1)/(2)* (1)/(3)\\\\\\i.e.\\\\\\P(E)* P(F)=(1)/(6)\\eq P(E\bigcap F)`

Hence, the events E and F are not independent.