Mathematics

Problem

A fair coin is tossed once and an unbiased die is rolled once. Event

E

: the coin shows Head. Event

F

: the die shows a number greater than

4

. Determine whether

E

and

F

are independent. a) Independent, because

P(E\cap F)=P(E)P(F)

b) Not independent, because

P(E\cap F)=\dfrac{1}{4}\neq P(E)P(F)

c) Independent, because

P(E\cap F)=P(E)+P(F)

d) Not independent, because

P(E\mid F)=\dfrac{1}{6}