HKCEE MATHEMATICS | 15 Probability |
P.1
1. 1990/II/26
There are 7 bags, 3 of which are empty and the remaining 4 each contains a ball. An additional ball is now put
into one of the bags at random. After that a bag is randomly selected. Find the probability of selecting an
empty bag.
2
7
A.
B.
3
7
C.
2. 1991/II/32
A fair die is thrown 3 times.
A.
1
3
B.
1
 
6
6
49
D.
12
49
E.
18
49
The probability that “6” occurs exactly once is
3
C.
1 1
×
3 6
D.
 1  5 
  
 6  6 
2
E.
 1  5 
  
 6  6 
2
3. 1992/II/33
Two cards are drawn randomly from five cards A, B, C , D and E . Find the probability that card A is drawn
while card C is not.
3
B.
A.
25
3
20
C.
4
25
D.
6
25
E.
4. 1993/II/31
Two fair dice are thrown. What is the probability of getting a total of 5 or 10?
1
5
1
7
A.
B.
C.
D.
E.
9
36
6
36
3
10
2
9
5. 1994/II/31
A box contains 5 eggs, 2 of which are rotten. If 2 eggs are chosen at random, find the probability that exactly
one of them is rotten.
2
A.
B.
5
3
5
C.
3
10
D.
6
25
E.
12
25
6. 1995/II/31
3
2
and the probability that B will hit it is . If each
5
3
fires once, what is the probability that they will both miss the target?
1
1
2
2
11
A.
B.
C.
D.
E.
3
4
5
15
15
In a shooting game, the probability that A will hit a target is
198
HKCEE MATHEMATICS | 15 Probability |
P.2
7. 1995/II/32
The figure shows that Mr. Chan has 3 ways to leave town X and Mr. Lee has 2 ways to leave town Y. Mr. Chan
and Mr. Lee leave town X and town Y respectively at the same time. If they select their ways randomly, find
the probability that they will meet on their way.
1
1
2
A.
B.
C.
2
3
3
D.
1
6
E.
5
6
8. 1996/II/34
There are 10 parcels. Two of them contain one pen each. If a man opens the parcels at random, what is the
probability that he can find the two pens by opening two parcels only?
1
1
1
1
A.
B.
C.
D.
25
45
50
90
E.
1
100
9. 1996/II/35
In a certain game, the probability that John will win is 0.3 . If he plays the game 3 times, find the probability
that he will win at least once.
A. 0.147
B. 0.441
C. 0.657
D. 0.9
E. 0.973
10. 1997/II/25
Two fair dice are thrown. Find the probability that the sum of the two numbers shown is 8.
1
1
1
1
5
A.
B.
C.
D.
E.
4
6
11
12
36
11. 1997/II/26
In a test, there are 3 questions. For each question, the probability that John correctly answers it is
the probability that he gets exactly 2 questions correct.
2
4
12
A.
B.
C.
3
25
25
D.
12
125
E.
2
. Find
5
36
125
12. 1998/II/35
Two cars are drawn randomly from five cards numbered 2 , 2 , 3 , 5 and 5 respectively. Find the probability that
the sum of the numbers on the cards drawn is 5.
1
2
1
2
4
A.
B.
C.
D.
E.
5
5
10
25
25
199
HKCEE MATHEMATICS | 15 Probability |
P.3
13. 1998/II/36
In a shooting game, the probability that Mr. Tung will hit the target is
that he will hit the target at least once.
1
2
B.
A.
9
9
C.
4
9
D.
2
. If he shoots twice, find the probability
3
2
3
E.
8
9
14. 1999/II/35
Two cards are drawn randomly from four cards numbered 1 , 2 , 3 and 4 respectively. Find the probability that
the sum of the numbers drawn is odd.
1
1
1
1
2
A.
B.
C.
D.
E.
6
4
3
2
3
15. 1999/II/36
Tom and Mary each throws a dart. The probability of Tom’s dart hitting the target is
2
. Find the probability of only one dart hitting the target.
5
2
3
7
A.
B.
C.
15
15
15
D.
11
15
16. 2000/II/21
Two fair dice are thrown. Find the probability that at least one “6” occurs.
1
1
5
7
A.
B.
C.
D.
3
6
18
36
E.
E.
1
while that of Mary’s is
3
13
15
11
36
17. 2000/II/22
A bag contains six balls which are marked with the numbers −3, −2, −1, 1, 2 and 3 respectively. Two balls are
drawn randomly from the bag. Find the probability that the sum of the numbers drawn is zero.
1
1
1
1
1
A.
B.
C.
D.
E.
30
10
5
3
2
18. 2001/II/35
Two cards are drawn randomly from five cards numbered 1, 2, 3, 4 and 4 respectively. Find the probability that
the sum of the two numbers drawn is even.
1
2
3
7
13
A.
B.
C.
D.
E.
2
5
10
10
25
19. 2001/II/36
A bag contains 2 black balls and 3 white balls. A boy randomly draws balls from the bag one at a time (without
replacement) until a white ball appears. Find the probability that he will make at least 2 draws.
A.
2
5
B.
3
5
C.
1
10
D.
200
3
10
E.
7
10
HKCEE MATHEMATICS | 15 Probability |
P.4
20. 2002/II/35
Two numbers are drawn randomly from five cards numbered 3, 4, 5, 6 and 7 respectively. Find the probability that
the product of the numbers drawn is even.
3
1
7
16
B.
C.
D.
A.
5
10
10
25
21. 2002/II/36
In a test, there are two questions. The probability that Mary answers the first question correctly is 0.3 and the
probability that Mary answers the second question correctly is 0.4. The probability that she answers at least one
question correctly is
A. 0.42
B.
0.46
C.
0.58
D.
0.88
22. 2003/II/34
A bag contains 2 black balls, 2 green balls and 2 yellow balls. Peter repeats drawing one ball at a time randomly
from the bag without replacement until a green ball is drawn. Find the probability that he needs at most 4 draws.
1
2
14
65
B.
C.
D.
A.
15
15
15
81
23. 2003/II/35
1232 is a 5-dight number, where is an integer from 0 to 9 inclusive. The probability that the 5-dight number
is divisible by 4 is
1
A.
3
B.
1
4
C.
1
5
D.
3
10
24. 2004/II/33
A bag contains 3 red balls and 4 green balls. If two balls are drawn randomly from the bag one by one without
replacement, then the probability that the two balls are of different colors is
2
4
12
24
A.
B.
C.
D.
7
7
49
49
25. 2004/II/34
Peter and May each throws a dart. The probability of Peter’s hitting the target is 0.2. The probability of May’s
hitting the target is 0.3. Find the probability of at least one dart hitting the target.
A.
0.38
B.
0.44
C.
0.5
D.
0.56
26. 2005/II/35
Bag X contains 1 white ball and 3 red balls while bag Y contains 3 yellow balls and 6 red balls. A ball is
randomly drawn from bag X and put into bag Y. If a ball is now randomly drawn from bag Y, then the
probability that the ball drawn is red is
1
2
21
A.
B.
C.
2
3
40
D.
27
40
201
HKCEE MATHEMATICS | 15 Probability |
P.5
27. 2005/II/36
If a fair die is thrown three times, then the probability that the three numbers thrown are all different is
5
17
125
215
A.
B.
C.
D.
9
18
216
216
28. 2006/II/32
Which of the following could be the probability of an event?
A.
π
3
B.
2005
2006
C.
–0.2006
D.
1.2006
29. 2006/II/33
Two fair dice are thrown. Find the probability that the sum of the two numbers thrown is a prime number.
A.
1
2
B.
5
11
C.
5
12
D.
7
18
30. 2006/II/52
One letter is chosen randomly from each of the two words ‘FORTY’ and ‘FIFTY’ . Find the probability that
the two letters chosen are the same.
A.
0.08
B.
0.16
C.
0.32
D.
0.48
31. 2006/II/53
There are two questions in a test. The probability that David answers the first question correctly is
1
and the
4
1
. Given that David answers at least one
3
probability that David answers the second question correctly is
question correctly in the test, find the probability that he answers the second question correctly.
A.
1
2
B.
2
3
C.
3
5
D.
4
5
32. 2007/II/33
Two numbers are randomly drawn at the same time from five cards numbered 1 , 2 , 3 , 4 and 5 respectively. Find
the probability that the sum of the numbers drawn is a multiple of 3.
A.
2
5
B.
3
10
C.
9
20
D.
9
25
33. 2007/II/53
A bag contains 8 black balls and 5 white balls. If two balls are drawn randomly from the bag one by one
without replacement, then the probability that the two balls are of the same colour is
A.
14
39
B.
19
39
C.
89
156
D.
202
89
169
HKCEE MATHEMATICS | 15 Probability |
P.6
34. 2007/II/54
One letter is chosen randomly from each of the two words ‘CUBE’ and ‘CONE’ . Find the probability that
the two letters chosen are different.
A.
1
4
B.
3
4
C.
1
8
D.
7
8
35. 2008/II/33
4is a 2-digit number, where is an integer from 0 to 0 inclusive. Find the probability that the 2-digit number
is a prime number.
A.
0.2
B.
0.3
C.
0.4
D.
203
0.5