PROBABILITY AND
STATISTICS PROBLEM SET
A survey of non healthy habits of 80 sophomore a. 0.84 b. 0.83 c. 0.87 d. 0.9
students of a certain seminary showed the following 11. A group of 3 people enter a theater after the lights
habits: head dimmed. They are shown to the correct group
45 drink alcoholic beverages; 19 of 3 seats by the usher. Each person holds a number
stay up late and smoke; stub. What is the probability that each is in the
42 stay up late correct seat according to the numbers on seat and
22 drink alcohol and stay up late; stub?
40 smoke cigarettes; a. 1/2 b. 2/3 c. 1/6 d. 1.3
9 practice clean 25 drink
alcohol and cigarette 12. The probability of getting a credit in an
1. How many drink alcohol only? examination is 1/3. If the three students are selected
A. 8 b. 10 c. 12 d. 14 at random, what is the probability that at least one of
2. How many drink alcohol and smoke but sleeps them got a credit?
early? a. 8/27 b. 20/27 c. 19/27 d. 22/27
A. 12 b. 15 c. 16 d. 18
3. How many do all non healthy habits? In the board exam 70% of taker is from Luzon, 20%
A. 9 b. 8 c. 10 d. 12 from Visayas, and 10% from Mindanao. If 50% from
Luzon passed, 40% from Visayas passed, and 50%
4. A fair die is tossed 180 times. Find the probability from Mindanao Passed.
P that the face 6 will appear between 29 and 32
times inclusive. 13. Determine the Probability that a random
a. 0.57 b. 0.31 c. 0.42 d. 0.5 examinee came from Luzon and Passed
a. 0.12 c. 0.5
5. Suppose 2% of the items made by a factory are b. 0.4 d. 0.35
defective. Find the probability P that there are 3
defective items in a sample of 100 items. 14. Determine the Probability that a random
a. 0.18 b. 0.24 c. 0.30 d. 0.26 examinee passed.
a. 0.10 c. 0.48
6. A box contains three coins with a head on each b. 1.4x10-3 d. 0.5
side, four coins with a tail on each side, and two fair
coins. If one of these nine coins is selected at 15. Given that the Examinee passed determine the
random and tossed once, what is the probability that probability that it came from Luzon
a head will appear? a. 0.73 c. 0.12
a. 1/3 b. 4/9 c. 5/9 d. 2/3 b. 0.35 d. 0.48
A and B play 12 games of chess of which 6 are won 16. The weight of the Student is Normally Distributed
by A, 4 are won by B, and 2 end in a draw. They with a mean of 50 kg and standard deviation of 5 kg.
agree to play a tournament consisting of 3 games. Determine the probability that the weight of student
Find the probability that: will fall between 40 kg to 60 kg.
a. 0.9545 c. 0.9304
7. Determine the probability two games end in a b. 0.9012 d. 0.9870
draw.
a. 5/72 b. 6/72 c. 7/72 d. 8/72 Two marbles are drawn in succession from the box
8. Determine the probability that all 3 games won by that contains 10 Red, 20 Blue and 15 Orange,
A. replacement being made after each drawing.
a. 6/72 b. 1/8 c. 3/72 d. 5/72
17. Find the probability that at least one is blue.
9. Determine the probability that A and B win a. 23/33 c. 104/225
alternately. b. 176/405 d. 92/135
a. 5/36 b. 4/36 c. 6/36 d. 3/36
18. Find the probability that at most one is red.
10. A student is taking two exams, one in Calculus a. 221/225 c. 26/81
and another in Physics. The probability that he will b. 52/81 d. 2/3
pass the Calculus exam is 0.75 and the probability
that he will fail Physics exam is 0.20. The probability
that he will pass both exams is 0.65. What is the
probability that he will pass either exams?
