Regents Prep: Math A
Multiple-Choice Questions
Regents Prep Math A: Topical Multiple-Choice Question Archive
Use of Topical Archive Multiple-Choice Questions
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Uncertainty (Probability): Question 1 of 15
A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss?
  1. 0
  2. 1/16
  3. 1/8
  4. 1/2

Correct Answer Number: 4

Explanation: The fourth toss is independent of the first three tosses - it has nothing to do with the first three tosses. Therefore, the probability remains one out of two.

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Uncertainty (Probability): Question 2 of 15
How many different three-member teams can be formed from six students?
  1. 20
  2. 120
  3. 216
  4. 720

Correct Answer Number: 1

Explanation: The answer is a combination (6C3) - Six things taken three at a time.

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Uncertainty (Probability): Question 3 of 15
How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once?
  1. 6
  2. 36
  3. 720
  4. 46,656

Correct Answer Number: 3

Explanation: There are 6 letters which can be used to fill the first position in the new word, 5 letters to fill the second position, 4 letters to fill the third positon, and so on. The answer is 6 factorial.

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Uncertainty (Probability): Question 4 of 15
If P(E) is the probability that an event will occur, which of the following must be false?
  1. P(E)=1
  2. P(E)=1/2
  3. P(E)=1/3
  4. P(E)= - 1

Correct Answer Number: 4

Explanation: Probabilities are restricted to the closed interval from 0 to 1. There are no negative probabilities.

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Uncertainty (Probability): Question 5 of 15
Evaluate 1!+2!+3!
  1. 5
  2. 6
  3. 9
  4. 10

Correct Answer Number: 3

Explanation: 1!=1 and 2!=2•1=2 and 3!=3•2•1=6. Therefore, the sum equals 1+2+6=9.

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Uncertainty (Probability): Question 6 of 15
From a group of 8 people, how many teams of 4 can be chosen?
  1. 32
  2. 70
  3. 500
  4. 1680

Correct Answer Number: 2

Explanation: Use combinations when order is not important. 7C3=70. Use your calculator.

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Uncertainty (Probability): Question 7 of 15
A standard deck of 52 cards is shuffled. What is the probability of choosing the 5 of diamonds?
  1. 1/5
  2. 1/13
  3. 5/52
  4. 1/52

Correct Answer Number: 4

Explanation: There is only one 5 of diamonds in the deck of 52 cards.

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Uncertainty (Probability): Question 8 of 15
A die is rolled. What is the probability that the number rolled is greater than 2 and even?
  1. 1/2
  2. 1/3
  3. 2/3
  4. 5/6

Correct Answer Number: 2

Explanation: Numbers greater than 2 are 3,4,5 and 6.
Numbers that are even are 2,4 and 6.
Numbers in both are 4 and 6. There are 2 values out of 6.
2/6=1/3

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Uncertainty (Probability): Question 9 of 15
A pair of dice is rolled. A possible event is rolling a multiple of 5. What is the probability of the complement of this event?
  1. 2/36
  2. 12/36
  3. 29/36
  4. 32/36

Correct Answer Number: 3

Explanation: Multiples of 5: 5, 10
There are 7 ways to roll a 5 or 10.
P(multiple of 5)=7/36
P(complement)=1-7/36=29/36

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Uncertainty (Probability): Question 10 of 15
Your state issues license plates consisting of letters and numbers. There are 26 letters and the letters may be repeated. There are 10 digits and the digits may be repeated. How many possible license plates can be issued with two letters followed by three numbers?
  1. 25000
  2. 67600
  3. 250000
  4. 676000

Correct Answer Number: 4

Explanation: 26 x 26 x 10 x 10 x 10 = 676000

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Uncertainty (Probability): Question 11 of 15
How many elements are in the sample space of rolling one die?
  1. 6
  2. 12
  3. 24
  4. 36

Correct Answer Number: 1

Explanation: {1,2,3,4,5,6}

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Uncertainty (Probability): Question 12 of 15
Evaluate: (9-4)!
  1. 362880
  2. 120
  3. 24
  4. 6

Correct Answer Number: 2

Explanation: (9-4)!=5!=5•4•3•2•1=120

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Uncertainty (Probability): Question 13 of 15
How many different 5-letter arrangements are there of the letters in the word DIGIT?
  1. 5
  2. 30
  3. 60
  4. 120

Correct Answer Number: 3

Explanation: The letter i repeats. Permutations are used. (5•4•3•2•1)/(2•1)=120

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Uncertainty (Probability): Question 14 of 15
Two cards are drawn at random from a standard deck of 52 cards, without replacement. What is the probability of drawing a 7 and a king in that order?
  1. 4/51
  2. 4/52
  3. 4/256
  4. 4/663

Correct Answer Number: 4

Explanation: There are 4 7's and 4 kings. 4P1•4P1
From a deck of 52 cards you want 2 cards. 52P2
Answer: 4/52•4/51 = 16/2652 = 4/663

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Uncertainty (Probability): Question 15 of 15
A movie theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased?
  1. 1
  2. 3
  3. 9
  4. 27

Correct Answer Number: 3

Explanation: 3 x 3 = 9

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