Online Practice Test 3a for MATH 166.

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Test Questions:

1. E and F are mutually exclusive if

    E È F = Æ
    E Ç F = Æ
    E È F = Æ AND E Ç F = Æ
    E È F ¹ Æ AND E Ç F ¹ Æ

2. An experiment consists of tossing a coin three times and observing the resulting sequence of 'heads' and 'tails.' How many different outcomes are possible? (i.e. what is the size of the sample space?)

    3
    5
    6
    8
    9

3. A pair of fair dice is cast. What is the probability that the sum of the numbers of the two dice is 8?

    1/36
    1/12
    1/2
    5/36
    7/36

4. Let S = {a, b, c, d, e, f} be the sample space associated with an experiment having the following probability distribution:
Outcome a b c d e f
Probability 1/6 1/4 1/12 1/12 1/3 1/12
What is the probability of the event E = {a, b}?

    1/10
    1/24
    5/12
    1/6
    10/24

5. Let E and F be two mutaully exclusive events and suppose P(E) = 0.1 and P(F) = 0.6. What is the value of P(EC Ç FC) ?

    0
    0.3
    0.7
    0.9
    1

6. Two cards are selected at random from a well-shuffled deck of cards (52 cards total). What is the probability that both cards are kings?

    2/52
    2/2652
    1/221
    188/221
    103/2652

7. A group of 3 people is selected at random. What is the probability that at least two of them were born in the same month?

    17/72
    3/12
    1/3
    8/12
    55/72

8. In a group of 500 college students, of which 300 were men and 200 were women, it was determined that 25 of the men and 2 of the women were color blind.
Given that a randomly selected student from this group is color blind, what is the probability that the student is a woman?

    25/27
    7/25
    1/1000
    2/27
    2/5

9. Given that events A, B, C are independent and P(A) = 0.4, P(B) = 0.5 and P(C) = 0.2. What is P(A Ç B Ç CC

    0.16
    0.4
    0.04
    1
    1.1

10. Light bulbs for GoodLook flashlights are manufactured in three locations and then shipped to the main plant for final assembly. Plants A, B and C supply 50%, 30% and 20%, respectively, of the light bulbs used. Quality inspection has determined that 1% of the bulbs produced at plant A are defective, 2% of the bulbs at plant B are defective and 2% of the bulbs at plant C are defective.
If a GoodLook flshlight is selected at random and the light bulb is found to be defective, what is the probability that the bulb was manufactured at plant C?

    about 0.4
    about 0.27
    about 0.33
    about 0.04
    this cannot be determined as there is not enough information

11. Let X denote the random variable that gives the sum that falls uppermost when two fair dice are cast. What is the expected value, E(X) of X.
(Hint: construct a probability distribution table).

    5
    6
    7
    8
    9