Download Probability Worksheet 2

STATISTICS
SUPPLEMENT
PROBABILITY
NAME:
DATE:
PERIOD:
If two events, A and B, are disjoint, then P(A or B) = P(A) + P(B)
Note: if A and B are not disjoint (aka joint), use a Venn Diagram
If two events A and B are independent, then P(A and B) = P(A) * P(B)
Note: If A and B are not independent (dependent), use a tree diagram
A. Answer each.
1. Josh has 18 black socks and 12 white socks. Every morning he chooses one sock
at random. After he’s pulled that one sock out, he chooses another sock at random –
and wears them!
a) Find probability both socks are white.
b) Find the probability both are black.
c) Find the probability that the first sock is white and the 2nd is black?
d) What is the probability his socks match?
e) What is the probability his socks don’t match?
2. A fair coin is tosses and a far die is rolled. Find the probability of each.
a) Flipping heads and rolling a “4”.
b) Flipping tails and rolling an even number.
3. M&M candies are 24% blue, 20% orange, 16% green, 14% yellow, 13% red, and
13% brown.
a) Verify this is a legitimate assignment of probabilities.
b) If you pick one M&M, what is the probability it will be blue or orange?
c) If you pick a handful of 5 M&Ms, what is the probability all 5 are blue?
4. On a given Sunday afternoon in September, both the Padres and Chargers have a
game. Based on thorough research, the probability the Chargers will win their game
is .70 and the probability the Padres win is .60.
a) If the results of the two games are independent, what is the probability they both
win?
b) What is the probability the Padres or Chargers win?
c) What is the probability that both lose (and I become very bitter)?
5. Delegates at a convention are classified according to their gender and their
political affiliation. The results are summarized in the following table.
Women
Republicans
210
Democrats
250
Independents 60
Total
520
Men
280
160
40
480
Total
490
410
100
1000
A = a random delegate is a man
B = a random delegate is a Republican
C = a random delegate is an Independent
a) P(A)
b) P(Ac)
c) P(B)
d) P(C)
e) P(A and B)
f) P(B or C)
g) P(A or B)
h) P(B and C)
i) Are the events A and B disjoint? Why or why not?
j) Are the events A and B independent? Why or why not?
6. Blood donations are routinely screened for AIDS. The ELISA test will provide a
positive test result on blood that does contain AIDS 97.8% of the time. ELISA will
correctly come back negative for blood that does not contain AIDS 92.2% of the
time. Recent estimates suggest about 0.50% of the population has AIDS. If a
randomly selected person has their blood screened, what is the probability of the
ELISA test coming back positive? Draw a tree diagram to help.