Conditional Probability Worksheet
ADVERTISEMENT
1
2
3Conditional Probability Worksheet
Most of the questions here were stolen from a textbook, not written by me.
1. The two events A and B are such that P(A) = 0.6, P(B) = 0.2, P(A | B) = 0.1. Calculate
the probabilities that
(a) both of the events occur;
0.02
(b) at least one of the events occur;
0.78
(c) exactly one of the events occurs;
0.76
(d) B occurs given that A occurs.
1
30
1
2. I travel to work by route A or route B. The probability that I chose route A is
. The
4
2
probability that I am late for work if I go via route A is
and the corresponding probability
3
1
for route B is
.
3
(a) What is the probability that I am late for work on Monday?
5
12
(b) Given that I am late for work, what is the probability that I went via route B?
3
5
3. Susan takes exams in Maths, French and History. The probabilities that she passes are
0.7, 0.8 and 0.6 respectively. Given that her performances in each subject are independent,
draw a tree diagram to show the possible outcomes. Find the probabilities that Susan
(a) fails all three examinations
0.024
(b) fails just one examination
0.452
(c) Given that Susan fails just one examination, find the probability that it is History
that she fails.
0.4956
4. Four coins are biased so that the probabilities of getting a head are 0.4, 0.48, 0.52 and
0.6. One coin is chosen at random and, on being tossed three times, gives three heads.
What is the probability that the coin chosen was the coin with the bias 0.52?
2197
8300
5. On a certain Pacific island, a particular disease is caught by one person in a thousand.
98% of those who have the disease respond positively to a diagnostic test, but 3% of those
who do not have the disease also respond positively to the same test (a ‘false positive’). If
a person selected at random responds positively to the test, what is the probability that
he actually has the disease?
0.03166
6. If P(A) = 0.5, P(B) = 0.7 and P(A ∪ B) = 0.8, find P(A | B).
4
7
7. A and B are independent events, and P(A) = 0.7 and P(B) = 0.2. What are
(a) P(B | A)
0.2
(b) P(A ∩ B)
0.14
(c) P(A ∪ B)?
0.76
8. Two dice are rolled. Given that there is at least one six, what is the probability that both
are sixes?
1
11
9. If there are 23 people in a room, find the probability that at least two share the same
birthday.
0.50729723432398 . . .
10. A parent at an all boys school was heard to say at a parents’ meeting that she had two
children. What is the probability that they are both boys?
1
3
1
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education