Probability Assignment
Round all answers to 4 decimal places.
1. What are independent events?
2. What are mutually exclusive events?
3. If P(N ) 
 
1
, determine P N .
4
4. In an experiment, two regular (6-sided) dice are rolled, event A
represents rolling a sum of 7. How many outcomes in the total sample
space represent the complement, A .
5. A 13-card hand is dealt from a well shuffled 52 card deck. What is the
probability that this hand will contain exactly two jacks?
6. What is the probability of drawing a heart or a face card in a single draw
from a standard deck of 52 cards?
7. If one of the 19 equally likely outcomes on sample space S is randomly
selected, find the probability that:
x
A
x
x
S







x
x x
x x x x
x x
x
x x
B x
x x
x
both A and B occur
A but not B occurs
neither A nor B occurs
at least one of A or B occurs
at most one of A or B occurs
A occurs given that B has occurred
B occurs given that A has occurred
8. What is the probability of getting four of a kind in a 5-hand poker hand?
9. Jar 1 has 3 red, 2 white, and 5 black balls. Jar 2 has 4 red, 5 white and 3
black balls. A die is rolled and if a 1 or 2 comes up, a ball is selected from
Jar 1; however if a 3, 4, 5, or 6 comes up, a ball is selected from Jar 2.


what is the probability of selecting a red ball?
if a red ball is selected, what is the probability that it came from
Jar 1?
10. Machine A produces 60% of a product while Machine B produces 40%. 3%
of the product from Machine A is defective, while 2% from Machine B is
defective. If a defective product is selected, what is the probability that
it was produced by Machine B?
11. A card is picked from a regular 52 card pack. It is not replaced, and
another card is drawn. What is the probability that the two cards will
both be aces?
12. The probability of a certain bowler getting a strike in one throw is 0.3.
What is the probability that they will get exactly 3 strikes out of 4
throws?
13. A multiple choice quiz has 10 questions, each with 4 possible answers.
What is the probability that a student will get at least 1 question correct
on the test by guessing?
14. There are 2 red cubes and 2 green cubes in a bag. Two cubes are taken
out, one at a time, and the colors recorded. Then the cubes are returned
to the bag. If the cubes are drawn 60 times, how often would you predict
that the cubes have different colors?
15. In a randomly chosen group of 24 people, what is the probability that at
least two have the same birthday?
16. A committee of six people is selected from 11 females and 9 males.



what is the probability that there is exactly four females on the
committee?
what is the probability that there is exactly four males on the
committee?
what is the probability that there is at least three females on the
committee?
17. A class of 30 students has 10 honour students and 13 athletes. Three of
the honour students are also athletes. One student is chosen at random.
Find the probability that this student is an athlete if it is known that the
student is not an honour student.
18. A medical test for leukemia is 98% accurate. Suppose 1% of the
population has leukemia, what is the probability that a person who tests
positive does have leukemia? What is the probability of obtaining a
“false-negative” result?
19. What is the probability that a 5-letter code made from A, B, C, D, and E
with no repeated letters:



is in alphabetical order?
starts with a vowel?
starts and ends with a vowel?
20. Eight students write a Math exam. What is the probability that Jean gets
the top mark, Kim gets the second highest mark, and Stacey gets the
third highest mark if all students are of equal ability?
21. A coin is weighted such that P(heads) =
2
. Calculate the probability of
3
getting 4 heads in 10 tosses of the coin.
22. Each letter of the alphabet is placed in a bag. One letter is drawn and not
replaced. If three letters are drawn without replacement, what is the
probability that all three letters chosen are NOT any of the five vowels,
a, e, i, o, u?