Conditional Events Worksheet
1. Given :
Determine:
2. Given:
P (A ∩ B ) = 0.5
P (B ) = 0.7
P (A | B )
P (T | S ) = 0.3
P (S ) = 0.1
Determine:
3. Given :
P (S ∩T
)
P (A ∩ B ) = 0.2
P (A ∩ C ) = 0.3
P (B ∩ C ) = 0.4
P (A ) = 0.4
P (B ) = 0.6
P (C ) = 0.7
Determine:
a) P (A | B )
b) P (B | C
c)
d)
4. Given:
)
P (C | A )
P (C | B )
P (A | B ) = 0.3
P (B | A ) = 0.4
P (A ∩ B ) = 0.2
Determine:
a) P (A )
b) P (B )
5. A die is rolled. Determine the probability that it is a 5 given that it is greater than 3.
6. A card is drawn from a deck of cards. Determine the probability that it is a jack
given that it is a face card.
7. Joel surveyed his class asking the question “Do you like school?”. The results are as
follows:
Liked
Male
12
Female
10
Total
22
Disliked
5
3
8
No Opinion
2
1
3
Total
19
14
33
Determine the probability that :
a) P (likes school|student is male )
b) P ( student is female|dislikes school)
8. A die is thrown twice. Determine the probability that the sum of the rolls is less
than 4 given that:
a) At least one of the rolls is a 1
b) the first roll is a 1
9. When a hockey team gets possession of the puck the following probabilities have been
estimated:
•
•
•
•
They carry the puck over the opposing blue line 0.6
They get a shot on net 0.3
They get a shot and score 0.01
Cross the blue line and score 0.005
Determine the probability that they score given that:
a) they cross the blue line
b) they get a shot away
10. Suppose that the two joker cards are left in a standard deck. One of the jokers is
red the other is black. A single card is drawn but not returned to the deck. Then a
second card is drawn. Determine the probability of drawing:
a)
b)
c)
d)
e)
f)
one of the jokers on the first and an ace on the second
a numbered card on the first and the red joker on the second
a queen on both
any black card on both
any card below 10 on the first and the same numbered card on the second
the red joker or a red ace on either draw
11. A survey of 1000 people were asked whether they wear eyeglasses while driving.
These people were also tested to see whether they need to wear eyeglasses while
driving. The results are displayed in the table below.
NEED to wear
while driving
Yes
No
Wear glasses while driving
yes
No
440
140
20
400
If a person is selected at random from this group of 1000 people determine the
probability that:
a)
b)
c)
d)
should wear eyeglasses while driving
wear eyeglasses while driving
wear glasses while driving even though they do not need to wear them
does not wear glasses while driving even though they need to wear them
Answers
5
7
2) 0.03
3)
1
a)
3
4
b)
7
3
c)
4
2
d)
3
4)
a) 1/2
b) 2/3
1
5)
3
1
6)
3
7)
12
a)
19
3
b)
8
8)
3
a)
11
1
b)
3
1)
9)
1
120
1
b)
30
a)
10)
a)
b)
c)
d)
e)
f)
11)
4
1431
2
159
2
477
13
53
16
477
52
477
29
50
23
b)
50
1
c)
50
7
d)
50
a)