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Class 10 Maths Chapter 14: Probability MCQs with answers

10 multiple-choice questions on Probability, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
A box at a sweet shop in Mathura holds 40 laddoos, of which 15 are kesar laddoos and the rest are plain. One laddoo is taken out at random. The probability that it is a kesar laddoo is
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Answer: (b) 38

P(kesar) = 15/40 = 3/8. 5/8 is the plain laddoos; 3/5 divides kesar by plain instead of by all 40; 1/4 would need only 10 kesar laddoos.

Question 2
Thirty raffle tickets at a school fete are numbered 1 to 30. One ticket is drawn at random. The probability that its number is a multiple of 31 is
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Answer: (d) 0

No number from 1 to 30 is a multiple of 31, so there are no favourable outcomes: P = 0/30 = 0, an impossible event.

Question 3
A packet has 12 pencils and every one of them is an HB pencil. A pencil is taken out at random. The probability that it is an HB pencil is
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Answer: (a) 1

All 12 outcomes are favourable: P = 12/12 = 1, a sure event. 12 cannot be a probability, since it exceeds 1.

Question 4
The probability that the morning bus from Bhopal reaches Indore late is 0.37. The probability that it is not late is
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Answer: (b) 0.63

P(not late) = 1 − P(late) = 1 − 0.37 = 0.63. 1.37 adds instead of subtracting; 0.73 reverses the digits.

Question 5
A die is thrown once. Which of the following is an elementary event?
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Answer: (c) getting a number greater than 5

Only 'a number greater than 5' has a single outcome, 6. An even number has 3 outcomes, a number less than 3 has 2, a prime number has 3.

Question 6
A card is drawn from a well-shuffled deck of 52 playing cards. The probability that it is a black ace is
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Answer: (c) 126

The black aces are the ace of spades and the ace of clubs: P = 2/52 = 1/26. 1/13 counts all four aces.

Question 7
Every token in a box is red, green or yellow. For a token drawn at random, P(red) = 14 and P(green) = 512. Then P(yellow) is
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Answer: (a) 13

The probabilities of the elementary events add to 1: P(yellow) = 1 − 1/4 − 5/12 = 12/12 − 3/12 − 5/12 = 4/12 = 1/3.

Question 8
In practice at a court in Kochi, a basketball player attempts 80 free throws and scores on 52 of them. The empirical probability that she scores on a free throw is
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Answer: (b) 1320

Empirical probability = 52/80 = 13/20. 7/20 is the misses; 0.52 treats 52 as a percentage; 20/13 exceeds 1 and is upside down.

Question 9
A token is drawn 'at random' from a box of tokens. This phrase means that
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Answer: (a) every token in the box is equally likely to be drawn

Drawing at random is a short way of saying that all the tokens are equally likely to be drawn.

Question 10
A letter is chosen at random from the letters of the word KOLKATA. The probability that it is the letter K is
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Answer: (c) 27

KOLKATA has 7 letters, 2 of them K: P = 2/7. 1/5 and 2/5 count only the 5 different letters, which are not equally likely.

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