IB Math SL – Year 2
Name______________________________________
HW 5 – Practice on Independent and Conditional Probability
Formulas:
1.
Independent : P( A  B)  P( A)  P( B)
P( A  B)
Conditional : P( A / B) 
P( B)
Cards are drawn from an ordinary deck with replacement. Find
a. P(2 Spades) _______________________________________________________________
b. P (7,10, Jack ) ______________________________________________________________
c. P (3 Kings ) _________________________________________________________________
2.
Cards are drawn from an ordinary deck without replacement. Find
a. P (3 Black ) _________________________________________________________________
b. P ( Jack , Queen , King ) _______________________________________________________
c. P (4 Kings ) _________________________________________________________________
d. P(2 Diamonds ) ____________________________________________________________
e. P( Heart , Diamond , and Spade) _____________________________________________
f. P (2 Sevens) ________________________________________________________________
g. P(6 Hearts ) _______________________________________________________________
3.
A doctor finds that the probability of performing surgery on his patients is 0.67. If the doctor
randomly selects 4 patients, find the probability that the doctor will perform surgery on the
patient.
4.
The probability that Miss Weaver will take a Christmas trip and travel by car is 0.67. The
probability that she will take a Christmas trip is 0.91. What is the probability that she will travel
by car given that she will take a Christmas trip.
5.
If 47% of all Americans like to swim, find the probability that if 6 Americans are selected at
random, all will like to swim.
6.
The probability that the band will win grand champion at a district contest and win 1st place at
state contest is 0.21. The probability that the band will win grand champion at a district contest
is 0.57. What is the probability that the band will win 1st place at state given that they win grand
champion at a district contest?
7.
Of the graduates from Clemson University, 17% want to teach math. If 2 of the graduates are
selected at random, what is the probability that both will teach math?
8.
The Triple Blood Test screens pregnant women for the genetic disorder, Down Syndrome. The
data shown below represents the outcomes of the blood test for a sample of 5282 women.
Negative
Result
6
3921
Total
Down Syndrome
Not Affected
Positive
Result
48
1307
Total
1355
3927
5282
54
5228
If a woman is selected at random, find these probabilities.
a.
down syndrome is present , given that the blood test had a positive result.
b.
down syndrome is present, given that the blood test had a negative result.
c.
a woman was not affected, given that she had a positive result.
d. P( Not Affected / NegativeTest )
e. P( Down Syndrome and Positive Test )
9.
Consider events A, B such that P (A)  0, P (A)  1, P (B)  0, and P (B)  1.
In each of the situations (a), (b), (c) below state whether A and B are
mutually exclusive (M);
independent (I);
neither (N).
(a)
P(A|B) = P(A)
(b)
P(A  B) = 0
(c)
P(A  B) = P(A)
Working:
Answers:
(a) ..................................................................
(b) ..................................................................
(c) ..................................................................
(Total 6 marks)
10.
The table below shows the subjects studied by 210 students at a college.
(a)
Year 1
Year 2
Totals
History
50
35
85
Science
15
30
45
Art
45
35
80
Totals
110
100
210
A student from the college is selected at random.
Let A be the event the student studies Art.
Let B be the event the student is in Year 2.
(i)
Find P(A).
(ii)
Find the probability that the student is a Year 2 Art student.
(iii)
Are the events A and B independent? Justify your answer.
(6)
(b)
Given that a History student is selected at random, calculate the probability
that the student is in Year 1.
(2)
(c)
Two students are selected at random from the college. Calculate the
probability that one student is in Year 1, and the other in Year 2.
(4)
(Total 12 marks)