Name: ______________________________
Review: Probability Rules
Key Formulas:
Provide each formula below:
A. General Addition Rule
B. Conditional Probability
Warm Up:
For each probability distribution below, find



P(A or B) using the General Addition Rule
P(B|A)
P(A|B)
C. P (A) = 0.7, P(B) = 0.4, P(A and B) = 0.25
D. P(A) = 0.45, P(B) = 0.8, P(A and B) = 0.3
E. P(A) = 0.61, P(B) = 0.18, P(A and B) = 0.07
F. P(A) = 0.2, P(B) = 0.5, P(A and B) = 0.2
Problems:
Complete each of the problems below. Show all work fully.
1.
Andrea is a very good student. The probability that she studies and
passes her mathematics test is 17
studies is 15
16
20
. If the probability that Andrea
, find the probability that Andrea passes her
mathematics test, given that she has studied.
2.
The probability that Janice smokes is 3
10
smokes and develops lung cancer is 4
15
. The probability that she
. Find the probability that
Janice develops lung cancer, given that she smokes.
3.
The probability that Sue will go to Mexico in the winter and to France
in the summer is 0.40 . The probability that she will go to Mexico in
the winter is 0.60 . Find the probability that she will go to France this
summer, given that she just returned from her winter vacation in
Mexico.
4.
A penny and a nickel are tossed. Find the probability that the penny
Shows heads, given that the nickel shows heads.
5.
A penny is tossed. Find the probability that it shows heads. Compare
this answer to your answer to #4 and explain the results.
6.
A spinner with dial marked as shown is spun once. Find the probability
that it points to an even number given that it points to a shaded
region:
a) directly
b) using conditional probability formula
7.
A family that is known to have two children is selected at random
from amongst all families with two children. Find the probability that
both children are boys, given that there is a boy in this family.
8.
A die is tossed. Find P(less than 5 | even) .
9.
A number is selected, at random, from the set 1,2,3,4,5,6,7,8 . Find:
a) P(odd )
b) P( prime | odd )
10.
A box contains three blue marbles, five red marbles, and four white
marbles. If one marble is drawn at random, find:
a) P(blue | not white )
b) P(not red | not white )
11.
A number is selected randomly from a container containing all the
integers from 10 to 50 . Find:
a) P(even | greater than 40)
b) P( greater than 40 | even)
c) P( prime | between 20 and 40)
12.
A coin is tossed. If it shows heads, a marble is drawn from Box 1,
which contains one white and one black marble. If it lands tails, a
marble is drawn from Box 2, which contains two white and one black
marble. Find:
a) P(black | coin fell heads )
b) P(white | coin fell tails )
13. The table below shows the medal distribution from the 2000 Summer Olympic games for the top four countries.
Country // Medal
Gold
Silver
Bronze
United States
39
25
33
Russia
32
28
28
China
28
16
15
Australia
16
25
17
TOTAL:
TOTAL:
a) Fill out the missing totals.
b) Find the probability that the winner won the gold medal, given that the winner was from the US.
c) Find the probability that the winner was from the US, given that she or he won a gold medal.
14. At a particular school with 200 male students, 58 play football, 40 play basketball and 8 play both. Find the
probability that a randomly selected male student plays basketball or football.
a) Draw a venn diagram representing the distribution of male students at the school.
b) Find the probability that a randomly selected male plays football but not basketball.
c) Find the probability that a randomly selected male plays basketball.
d) Find the probability that a randomly selected male plays football and basketball.
e) Find the probability that a randomly selected male plays football or basketball.
f)
Find the probability that a randomly selected male student plays neither sport.
g) Find the probability that a randomly selected male plays football given that he plays basketball.
h) Find the probability that a randomly selected male plays basketball given the he plays football.
Answers:
A. P(A or B) = P(A) + P(B) – P(A and B)
B. P(B|A) = P(A and B) / P(A)
C.
P(A or B) = 0.85
P(B|A) = 0.36
P(A|B) = 0.63
D.
P(A or B) = 0.95
P(B|A) = 0.67
P(A|B) = 0.38
E.
P(A or B) = 0.72
P(B|A) = 0.11
P(A|B) = 0.39
F.
P(A or B) = 0.5
P(B|A) = 1
P(A|B) = 0.4
1.
68
= 0.91
75
2.
8
= 0.89
9
3.
2
= 0.67
3
4.
1
= 0.5
2
5.
1
= 0.5, heads appearing is independent
2
6.
a)
8.
1
1
= 0.5 b)
= 0.5
2
2
2
= 0.67
3
7.
9.
a)
3
= 0.375 11.
8
1
= 0.33
3
1
= 0.5
2
b)
3
= 0.75
4
1
= 0.5
2
5
4
= 0.24 c)
= 0.21
19
21
10.
a)
3
= 0.375
8
12.
a)
1
= 0.5
2
13.
a) 39 / 97 = 0.40
14.
a) Check with a partner b) 50 / 200 = 0.25
c) 40 / 200 = 0.20
d) 8 / 200 = 0.04
e) 90 / 200 = 0.45
g) 8 / 40 = 0.20
h) 8 / 58 = 0.14
b)
b)
a)
b)
2
= 0.67
3
b) 39 / 115 = 0.34
f) 110 / 200 = 0.55