AP Statistics / Mr. Hansen
Dec. 1, 2000

Name: ________________________

1.

There are two ways of checking to see if events A and B are independent. One is to test the IMI rule to see if it works; in other words, is __________ equal to _______________ ? The other is to see whether A’s probability remains unchanged if you know that B has occurred; in other words, is _______________ equal to the unconditional probability ____________ ?

2.

Show that the two methods in #1 are equivalent.

3.

If Q = the event of drawing a queen (single draw) and R = the event of drawing a red card (single draw), and if we are using a standard, well-shuffled 52-card deck, then
P(Q) = ______ (no need to show work)
P(R) = ______ (no need to show work)
P(Q Ç R) = ______ (no need to show work)
Does P(Q Ç R) equal P(Q) · P(R)? Why or why not (use one of the terms listed above)? ___________________________________________________
P(Q È R) = ______ (no need to show work)
Does P(Q È R) equal P(Q) + P(R)? Why or why not (use one of the terms listed above)? ___________________________________________________
P(Q | R) = ______ (no need to show work)
P(R | Q) = ______ (no need to show work)

4.(a)

If A and B are independent events with nonzero probabilities, how often does it happen that P(A and B) = P(A) + P(B)? ______________

(b)

If P(C) = c, what are the possible values for c? Answer: between _____ and _____, inclusive.

(c)

If C and D are independent events with P(C) = c and P(D) = 0.5, show that it is impossible to have P(C and D) = P(C) + P(D).