To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Conditional Probability Worksheet

Conditional Probability Worksheet
  • Page 1
 1.  
The frequency table shows the results from a poll conducted about reading the newspaper in the morning.

AdultChild
Reads3517
Does not read1223


Use the data to find P (Reads Newspaper | child)
a.
15 40
b.
17 40
c.
23 40
d.
12 47


Solution:

The sample space for child is 17 + 23 = 40.

Among them, 17 read the newspaper in the morning.

So, P (Reads newspaper | Child) = 17 / 40


Correct answer : (2)
 2.  
The frequency table shows the results from a poll conducted about reading the newspaper in the morning.

AdultChild
Reads3517
Does not read1223


Use the data to find P (Does not read Newspaper | Adult).
a.
12 17
b.
12 87
c.
12 40
d.
12 47


Solution:

The sample space for adult is 35 + 12 = 47.

Among them, 12 do not read newspaper in the morning.

So, P (does not read newspaper | Adult) = 12 / 47


Correct answer : (4)
 3.  
The table shows the population information of the percentage of male and female population in the U.S., in the year 2000, according to a census.

Under 18Over 18
Male26.873.2
Female24.675.4


Using the table find:P (Male | Under 18).
a.
2.2%
b.
26.8%
c.
18.03%
d.
52.1%


Solution:

P (Male | under 18) = 26.8% / (26.8%+24.6%)

0.268(0.268 + 0.246) = 0.521

The probability that a person under 18 will be male is 52.1%.


Correct answer : (4)
 4.  
A math teacher gave her class two tests. 76% of the class passed the first test. 58% of the class passed both tests. Find the probability that a student who passed the second test, given that he passed the first test.
a.
1.31
b.
0.58
c.
1.00
d.
0.76


Solution:

P (passes second test | passes first test) = P (Passes first and second test)P (Passes first test)
[Use P (B | A) = P (A and B)P (A).]

= 0.580.76 = 0.76


Correct answer : (4)
 5.  
The table shows the population information of the percentage of male and female population in the U.S., in the year 2000, according to a census.

Under 18


Solution:

P (Female | over 18) = 75.4%(73.2% + 75.4%) = 0.754(0.732 + 0.754)

= 0.507

The probability that a person over 18 is female is 50.7%.


Correct answer : (0)
 6.  
The frequency table shows the school enrolment (in thousands) in the year 2000. Let C represents california.
Pre primaryElementary or high schoolCollege or graduate school
California110164722557
New Jersey3031444470

Use the table to find P(C).
a.
79%
b.
82%
c.
61%
d.
91%


Solution:

The probability that a person enrolled in a school belongs to California = P(C)

P (C) = 1101 + 6472 + 25571101 + 6472 + 2557 + 303 + 1444 + 470

= 1013012347 = 0.8204

P (C) = 82.04% 82%


Correct answer : (2)
 7.  
The frequency table shows the school enrolment (in thousands) in the year 2000.
Let E represents elementary school.
Pre PrimaryElementary or high schoolCollege or graduate school
California110164722557
New Jersey3031444470

Use the table to find P(E).
a.
25.57%
b.
11.01%
c.
14.44%
d.
64.11%


Solution:

P (E) = the probability that a person is enrolled in elementary school of California or New Jersey.

P (E) = 6472 + 14441101 + 6472 + 2557 + 303 + 1444 + 470 = 7916 / 12347 = 0.6411

P (E) = 64.11%


Correct answer : (4)
 8.  
The frequency table shows the school enrolment (in thousands) in the year 2000.
Let C represents california and G represents graduate school.
Pre PrimaryElementary or high schoolCollege or graduate school
California110164722557
New Jersey3031444470

Use the table to find P(C and G).
a.
20.7%
b.
31.68%
c.
25.24%
d.
61.9%


Solution:

P (C and G) = 25571101 + 6472 + 2557 + 303 + 1444 + 470 = 2557 / 12347 = 0.207

The probability that a person enrolled in a graduate school of California is 20.7%


Correct answer : (1)
 9.  
The frequency table shows the school enrolment (in thousands) in the year 2000.
Let N represents New Jersey and R represents Pre primary school.
Pre PrimaryElementary or high schoolCollege or graduate school
California110164722557
New Jersey3031444470

Use the table to find P(R | N).
a.
76%
b.
13.9%
c.
18%
d.
15.7%


Solution:

P(R and N) = 3031101 + 6472 + 2557 + 303 + 1444 + 470 = 303 / 12347 = 0.025

P(N) = 303 + 1444 + 4701101 + 6472 + 2557 + 303 + 1444 + 470 = 221712347 = 0.180

P(R | N) = 0.025 / 0.18 = 0.139
[Use P(R | N) = P(R and N)P(N).]

The probability that a person enrolls in primary school, given that the person is from New Jersey is 13.9%.


Correct answer : (2)
 10.  
The frequency table shows the school enrolment (in thousands) in the year 2000.
Let C represents California and G represents graduate school.
Pre PrimaryElementary or high schoolCollege or graduate school
California110164722557
New Jersey3031444470

Use the table to find the probability that a person is from California, given that he is in graduate school.
a.
64.7%
b.
64.1%
c.
84.5%
d.
52.4%


Solution:

The required probability can be described by the notation P(C | G).

P (C | G) = P (C and G)P (G)
[Use P (B | A) = P (A and B)P (A).]

P (C and G) = 25571101 + 6472 + 2557 + 303 + 1444 + 470 = 255712347 = 0.207

P (G) = 2557 + 4701101 + 6472 + 2557 + 303 + 1444 + 470 = 302712347 = 0.245

P (C | G) = 0.2070.245 = 0.845

The probability that a person is from California given that he is in graduate school is 84.5%.


Correct answer : (3)
  • 1
  • 2
  • 3
  • Next »

  • *AP and SAT are registered trademarks of the College Board.