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Free Arithmetic MCQs with Answers

1,060 Arithmetic MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Arithmetic applies numerical operations to percentages, ratios, proportions, profit and loss, averages, and practical rate problems. Questions also involve time, speed and distance, and time and work, requiring careful use of units, direct and inverse relationships, weighted values, and work-rate methods rather than algebraic manipulation.

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1,060 questions · page 41 of 53

801. Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is_________?

  • A. 10/17
  • B. 10/19
  • C. 46/105
  • D. Cannot be determined

Explanation: The actual set of 15 consecutive numbers is not given, and the number of primes and odd numbers can change with the starting number.

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Correct answer: Cannot be determined

802. A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?

  • A. 4/9
  • B. 5/9
  • C. 7/9
  • D. 8/9

Explanation: There are 5 x 4 = 20 favorable pairs with one white and one red ball, out of C(9,2) = 36 total pairs. Thus the probability is 20/36 = 5/9.

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Correct answer: 5/9

803. A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?

  • A. 3/22
  • B. 4/21
  • C. 2/21
  • D. 1/14

Explanation: There are 3 blue plus 2 yellow marbles, so 5 favorable marbles. The probability that both selected marbles come from these five is…

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Correct answer: 2/21

804. A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?

  • A. 1/455
  • B. 2/455
  • C. 1/91
  • D. 4/455

Explanation: All three must be selected from the 3 blue marbles, giving C(3,3) = 1 favorable selection.

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Correct answer: 1/455

805. A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?

  • A. 17/91
  • B. 33/91
  • C. 51/91
  • D. 65/91Islamic Studies Quiz

Explanation: There are 12 non-blue marbles, so the favorable selections are C(12,4) = 495.

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Correct answer: 33/91

806. A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good.

  • A. 6/63
  • B. 2/63
  • C. 125/126
  • D. 1/126

Explanation: The complement of at least one good bulb is selecting all four defective bulbs.

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Correct answer: 125/126

807. A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.

  • A. 62/63
  • B. 125/126
  • C. 1/63
  • D. 1/126

Explanation: To select all four defective bulbs, there is C(4,4) = 1 favorable selection.

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Correct answer: 1/126

808. Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is -.

  • A. 5/9
  • B. 5/12
  • C. 1/36
  • D. 7/12

Explanation: Choose the repeated number in 6 ways, the different number in 5 ways, and the position of the different die in 3 ways.

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Correct answer: 5/12

809. Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is__________?

  • A. 7/12
  • B. 5/9
  • C. 1/36
  • D. 5/12

Explanation: For three different results, the first die has 6 choices, the second 5 remaining choices, and the third 4 remaining choices.

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Correct answer: 5/9

810. Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -.

  • A. 1/216
  • B. 1/36
  • C. 5/9
  • D. 5/12

Explanation: All three dice can show the same number in 6 outcomes: 111, 222, through 666.

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Correct answer: 1/36

811. A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is__________?

  • A. 25/42
  • B. 9/20
  • C. 10/23
  • D. 41/42

Explanation: The favorable cases are exactly 2 apples or exactly 3 apples: C(5,2) x C(4,1) + C(5,3) = 10 x 4 + 10 = 50.

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Correct answer: 25/42

812. A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.

  • A. 8/15
  • B. 2/5
  • C. 3/5
  • D. 7/15

Explanation: Same-colour selections are two green or two white: C(7,2) + C(8,2) = 21 + 28 = 49.

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Correct answer: 7/15

813. If six persons sit in a row, then the probability that three particular persons are always together is____________?

  • A. 1/20
  • B. 3/10
  • C. 1/5
  • D. 4/5

Explanation: Treat the three specified persons as one block. The block plus the other three people gives 4!

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Correct answer: 1/5

814. If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is__________?

  • A. 19/52
  • B. 17/52
  • C. 5/13
  • D. 4/13

Explanation: There are 13 spades and 4 kings, but the king of spades is counted twice, so favorable cards = 13 + 4 - 1 = 16.

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Correct answer: 4/13

815. If four coins are tossed, the probability of getting two heads and two tails is__________?

  • A. 3/8
  • B. 6/11
  • C. 2/5
  • D. 4/5Education

Explanation: The two heads can be placed among four tosses in C(4,2) = 6 ways. Since four coins have 2^4 = 16 equally likely outcomes, the probability…

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Correct answer: 3/8

816. If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is__________?

  • A. 1/4
  • B. 1/2
  • C. 3/4
  • D. 3/5

Explanation: Each die has 3 even and 3 odd faces, so the chance of an even-odd arrangement is (1/2 x 1/2) + (1/2 x 1/2) = 1/2, allowing for either die…

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Correct answer: 1/2

817. Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is_____________?

  • A. 1/2
  • B. 16/19
  • C. 4/5
  • D. 17/20

Explanation: Among 1 to 20, there are 10 even numbers and 8 primes: 2, 3, 5, 7, 11, 13, 17 and 19.

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Correct answer: 17/20

818. If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is___________?

  • A. 1/25
  • B. 1/2
  • C. 4/13
  • D. 1/10

Explanation: The perfect cubes from 1 to 100 are 1, 8, 27 and 64, so there are 4 favourable outcomes out of 100. Thus the probability is 4/100 = 1/25.

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Correct answer: 1/25

819. A coin is tossed live times. What is the probability that there is at the least one tail?

  • A. 31/32
  • B. 1/16
  • C. 1/2
  • D. 1/32

Explanation: For five fair tosses, the complement of at least one tail is getting no tails, meaning five heads, with probability (1/2)^5 = 1/32.

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Correct answer: 31/32

820. The probability that a number selected at random from the first 50 natural numbers is a composite number is__________?

  • A. 21/25
  • B. 17/25
  • C. 4/25
  • D. 8/25

Explanation: From 1 to 50 there are 15 primes, and 1 is neither prime nor composite.

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Correct answer: 17/25
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