Multiple Choice
Identify the choice that best
completes the statement or answers the question.
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1.
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Which pair of sets represents equal sets?
A. | N, the set of natural numbers, and I, the set of
integers | B. | T, the set of all triangles, and C, the set of all
circles | C. | N, the set of natural numbers, and P, the set of positive
integers | D. | none of the above |
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2.
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Which Venn diagram correctly represents the situation described?
Rahim
described the set as follows:
• M = {all of the foods he eats}
• D =
{his favourite desserts}
• V = {his favourite vegetables}
• F = {his
favourite fruits}
Assume Rahim likes some fruit for dessert.
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3.
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How many possible ways can you draw a single card from a standard deck and get
an even number?
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4.
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Evaluate.
8! + 1!
A. | 40 321 | B. | 5041 | C. | 40
123 | D. | 16 777 217 |
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5.
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Identify the expression that is equivalent to the following: 
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6.
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Which of the following is equivalent to  ?
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7.
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Which of the following is equivalent to  ?
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8.
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Julie draws a card at random from a standard deck of 52 playing cards. Determine
the probability of the card being a diamond.
A. | 0.250 | B. | 0.500 | C. |
0.625 | D. | 0.750 |
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9.
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Dora tosses four coins. Determine the probability that at least two coins will
land as heads.
A. | 37.52% | B. | 46.30% | C. | 68.75% | D. | 74.17% |
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10.
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Jake and Agnes are playing a board game. If a player rolls a sum greater than 9
or a multiple of 6, the player gets a bonus of 50 points. Determine the probability of rolling a sum
greater than 9.
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11.
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Select the events that are mutually exclusive.
A. | Drawing a red card or drawing a diamond from a standard deck of 52 playing
cards. | B. | Rolling a sum of 8 or rolling an even number with a pair of six-sided dice, numbered
1 to 6. | C. | Drawing a black card or drawing a Queen from a standard deck of 52 playing
cards. | D. | Drawing a 3 or drawing an even card from a standard deck of 52 playing
cards. |
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12.
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Sarah draws a card from a well-shuffled standard deck of 52 playing cards. Then
she draws another card from the deck without replacing the first card. Determine the probability that
both cards are NOT face cards.
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13.
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Carlo goes to the gym and does two different cardio workouts each day. His
choices include using a treadmill, a stationary bike, and running the track. Determine the
probability that the next time Carlo goes to the gym will use the stationary bike and then run the
track.
A. | 16.7% | B. | 26.1% | C. | 33.4% | D. | 41.9% |
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14.
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A four-sided red die and a four-sided green die are rolled. Determine the
probability of rolling a 1 on the red die and rolling a 3 on the green die.
A. | 0.23% | B. | 3.09% | C. | 6.25% | D. | 10.16% |
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15.
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Select the independent events.
A. | P(A) = 0.22, P(B) = 0.39, and P(A Ç B) = 0.072 | B. | P(A) = 0.18, P(B) =
0.7, and P(A Ç B) = 0.163 | C. | P(A) =
0.51, P(B) = 0.1, and P(A Ç B) =
0.069 | D. | P(A) = 0.9, P(B) = 0.23, and P(A Ç B) = 0.207 |
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Short Answer
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1.
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The city surveyed 3000 people about how they travel to work.
• 1978
took public transit (P)
• 1494 drove (D)
• 818 cycled
(C)
• 731 took public transit and drove only
• 298 took public transit and
cycled only
• 27 drove and cycled only
• 164 used all three modes of
transportation
How many people did not cycle or use public transit? Write your answer using set
notation.
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2.
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From a committee of 12 people, 3 of these people are randomly chosen to be
president, vice-president, and secretary. Determine, to the nearest hundredth of a percent, the
probability that Pavel, Rashida, and Jerry will be chosen.
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3.
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Two cards are drawn without being replaced, from a standard deck of 52 playing
cards. Determine, to the nearest hundredth of a percent, the probability of drawing a spade and a
diamond.
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Problem
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1.
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Use a truth table to determine whether the following statement is biconditional:
“ If  , then x is greater than 1.”
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2.
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If a conditional statement is false, what do you know about its contrapositive?
Explain.
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3.
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On Tuesday, the weather forecaster says that there is a 40% chance of snow on
Wednesday and a 50% chance of snow on Thursday. The forecaster also says that there is a 10% chance
of snow on both Wednesday and Thursday. Determine the probability that there will be snow on
Wednesday or on Thursday. Show your work.
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