Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die.
Pick:	A) 1/2	B) 1/6	C) 0	D) 5/6	E) 1
Determine if E and F are independent.   P(E|F) = the probability of event E occurring given that event F has already occurred   P(E|F) ≠ P(E) as P(E) is changed if it is given that F occurs.   Consequently, P(E∩F) ≠ P(E)P(F) since the events are not independent. As a result, P(E∩F) ≠ 1/4 = P(E)P(F)   We must use the more complex formula for finding the intersection of E and F:   P(E∩F) = P(F)P(E|F)   P(F) = the probability of event F occurring   The probability of rolling a 1, 2, or 3 is 3/6 = 1/2   P(E|F) = the probability of event E occurring given that event F has already occurred   If event F already occurred, we are limited to the numbers 1, 2, or 3. Within this range of 3 possible numbers, only one number--namely, 2--is an even number. Therefore, P(E|F) = 1/3   P(E∩F) = P(F)P(E|F) = (1/2) * (1/3) = 1/6   Answer 1/6
<result>B</result>
Event E is defined to be rolling an even number on a 6-sided die and Event F is defined to be rolling a 1, 2 or 3. Calculate the probability of rolling a die such that events E and F occur simultaneously on a single roll of the die.