Chapter 14 · Class 10 CBSE · MCQ Test
Probability MCQ Test — Class 10 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Probability — MCQ Questions
1Which of the following statements about the probability of an event E is always true?
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Answer: 0 ≤ P(E) ≤ 1
Hint: Remember that probability is a measure of the likelihood of an event, which can range from impossible to certain.
Solution:
The probability of any event E, denoted as P(E), must be a value between 0 and 1, inclusive.
P(E) = 0 means the event is impossible, and P(E) = 1 means the event is certain.
Therefore, the statement 0 ≤ P(E) ≤ 1 is always true for any event.
2A fair six-sided die is rolled once. What is the probability of getting an even number?
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Answer: 1/2
Hint: First, list all possible outcomes when a die is rolled, then identify the outcomes that are even numbers.
Solution:
The total number of possible outcomes when rolling a fair die is {1, 2, 3, 4, 5, 6}, so Total Outcomes = 6.
The favorable outcomes for getting an even number are {2, 4, 6}, so Favorable Outcomes = 3.
The probability of getting an even number is (Favorable Outcomes) / (Total Outcomes) = 3/6 = 1/2.
3A student calculated the probability of an event and reported it as -0.5. Which of the following statements about this calculation is true?
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Answer: The calculation is incorrect because probability cannot be negative.
Hint: Recall the fundamental property of probability concerning its possible values.
Solution:
The probability of any event must be a value between 0 and 1, inclusive (0 ≤ P(E) ≤ 1).
A negative probability value is not possible for any event, nor can it be greater than 1.
Therefore, the student's calculation resulting in -0.5 is incorrect.
4Consider two events: Event A is 'getting a sum of 13 when rolling two fair dice' and Event B is 'getting a number less than 7 when rolling a single fair die'. Which of the following correctly describes these events?
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Answer: A is an impossible event, B is a sure event.
Hint: Think about the maximum sum achievable with two dice and the range of numbers on a single die.
Solution:
For Event A: The maximum sum possible when rolling two fair dice is 6 + 6 = 12. Therefore, getting a sum of 13 is an impossible event, so P(A) = 0.
For Event B: When rolling a single fair die, the possible outcomes are {1, 2, 3, 4, 5, 6}. All these numbers are less than 7. Therefore, getting a number less than 7 is a sure event, so P(B) = 1.
Thus, A is an impossible event and B is a sure event.
5A bag contains 3 red, 5 black, and 2 white balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is NOT black?
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Answer: 1/2
Hint: First, find the total number of balls. Then, identify the number of balls that are NOT black.
Solution:
Total number of balls in the bag = 3 (red) + 5 (black) + 2 (white) = 10 balls.
Number of balls that are NOT black = Number of red balls + Number of white balls = 3 + 2 = 5 balls.
The probability of drawing a ball that is NOT black = (Number of non-black balls) / (Total number of balls) = 5/10 = 1/2.
6Which of the following scenarios involves outcomes that are NOT equally likely?
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Answer: Predicting tomorrow's weather (sunny, cloudy, rainy).
Hint: Equally likely means each outcome has the same chance of occurring. Consider if all possibilities in each scenario have an equal likelihood.
Solution:
A) Drawing a number from 1 to 10: Each number (1, 2, ..., 10) has a 1/10 chance, so outcomes are equally likely.
B) Rolling a fair die: Each face (1, 2, 3, 4, 5, 6) has a 1/6 chance, so outcomes are equally likely.
C) Tossing a fair coin: Heads and Tails each have a 1/2 chance, so outcomes are equally likely.
D) Predicting tomorrow's weather: The probabilities of sunny, cloudy, or rainy weather are generally not equal, as they depend on geographical location, season, etc. Therefore, the outcomes are NOT equally likely.
7The probability that it will rain tomorrow is 0.35. What is the probability that it will NOT rain tomorrow?
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Answer: 0.65
Hint: Remember the relationship between the probability of an event happening and the probability of it not happening.
Solution:
Let E be the event that it will rain tomorrow. So, P(E) = 0.35.
The event that it will NOT rain tomorrow is the complementary event, denoted as E'.
The sum of the probability of an event and its complementary event is always 1: P(E) + P(E') = 1.
Therefore, P(E') = 1 - P(E) = 1 - 0.35 = 0.65.
8In a box, there are some green and 12 blue pens. The probability of picking a green pen is 1/4. How many green pens are there in the box?
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Answer: 4
Hint: Let 'x' be the number of green pens. Express the total number of pens and the probability of picking a green pen in terms of 'x'.
Solution:
Let the number of green pens be 'x'.
Number of blue pens = 12.
Total number of pens = x + 12.
The probability of picking a green pen is (Number of green pens) / (Total number of pens) = x / (x + 12).
We are given that P(Green) = 1/4. So, x / (x + 12) = 1/4.
Cross-multiply: 4x = x + 12.
Subtract x from both sides: 3x = 12.
Divide by 3: x = 4. Therefore, there are 4 green pens in the box.
9A card is drawn at random from a well-shuffled deck of 52 playing cards. What is the probability of drawing a king of hearts?
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Answer: 1/52
Hint: In a standard deck, how many 'King of Hearts' cards are there?
Solution:
Total number of cards in a well-shuffled deck = 52.
There is only one King of Hearts in a standard deck of 52 cards.
Number of favorable outcomes (drawing a King of Hearts) = 1.
Probability = (Favorable Outcomes) / (Total Outcomes) = 1/52.
10A coin is tossed twice. A student claims that the probability of getting 'exactly one head' is 1/3 because there are three possible outcomes: (HH), (HT), (TT). Is the student's reasoning correct?
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Answer: No, the reasoning is incorrect because there are actually four equally likely outcomes.
Hint: List all possible unique sequences of outcomes for tossing a coin twice, and consider if they all have the same probability.
Solution:
When a coin is tossed twice, the complete sample space of equally likely outcomes is {(HH), (HT), (TH), (TT)}.
There are 4 equally likely outcomes, not 3. The student incorrectly combined (HT) and (TH) or considered them as one outcome without realizing their distinct nature.
The favorable outcomes for 'exactly one head' are (HT) and (TH), so there are 2 favorable outcomes.
The correct probability of getting 'exactly one head' is 2/4 = 1/2, not 1/3.
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Tips for Probability MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Probability MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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