Chapter 10 (Balbharati) · Class 9 Maharashtra SSC · MCQ Test
Probability (संभाव्यता) MCQ Test — Class 9 Maharashtra SSC
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Probability (संभाव्यता) — MCQ Questions
1Which of the following statements correctly defines the experimental probability of an event E?
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Answer: B) P(E) = (Number of times E happened) / (Total number of trials)
Hint: Recall the formula for experimental probability, which is based on observations from actual experiments or trials.
Solution:
Experimental probability is calculated from actual experiments or observations.
It is defined as the ratio of the number of times an event occurs to the total number of trials conducted.
Therefore, P(E) = (Number of times E happened) / (Total number of trials).
2Which of the following values cannot be the probability of an event?
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Answer: C) 1.5
Hint: Remember that the probability of any event must always lie within a specific numerical range.
Solution:
The probability of any event E, denoted as P(E), must always satisfy the condition 0 ≤ P(E) ≤ 1.
This means probability can be 0 (impossible event), 1 (certain event), or any fraction or decimal between 0 and 1.
Values like 0.7, 1/2 (which is 0.5), and 0 all fall within this valid range.
However, 1.5 is greater than 1, so it cannot be a valid probability for any event.
3If P(E) is the probability of an event E, what is the probability of the event 'not E'?
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Answer: A) 1 - P(E)
Hint: Consider that an event either happens or it doesn't. The sum of these two possibilities must cover all outcomes.
Solution:
For any event E, the event 'not E' (also called the complementary event, E') represents all outcomes where E does not occur.
The sum of the probabilities of an event and its complement is always 1, meaning P(E) + P(not E) = 1.
From this relationship, we can find the probability of 'not E' by rearranging the equation.
Therefore, P(not E) = 1 - P(E).
4A coin is tossed 200 times. The outcomes are recorded as follows: Heads: 110 times, Tails: 90 times. What is the experimental probability of getting a Head?
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Answer: B) 11/20
Hint: To find the experimental probability, you need the number of times the desired event occurred divided by the total number of trials.
Solution:
The total number of trials (coin tosses) is given as 200.
The number of times the event 'getting a Head' occurred is 110.
The experimental probability P(Head) = (Number of Heads) / (Total number of tosses).
P(Head) = 110 / 200 = 11 / 20.
5A die is rolled 300 times and the outcomes are noted: Outcome | 1 | 2 | 3 | 4 | 5 | 6 --------|---|---|---|---|---|--- Frequency | 50 | 45 | 55 | 60 | 40 | 50 What is the experimental probability of getting an outcome greater than 4?
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Answer: B) 3/10
Hint: First, identify which outcomes are 'greater than 4' and sum their corresponding frequencies. Then, divide by the total number of rolls.
Solution:
The total number of trials (die rolls) is 300.
The outcomes that are greater than 4 are 5 and 6.
The frequency of outcome 5 is 40. The frequency of outcome 6 is 50.
The total number of times 'getting an outcome greater than 4' occurred = Frequency(5) + Frequency(6) = 40 + 50 = 90.
Experimental probability P(outcome > 4) = (Number of times outcome > 4 occurred) / (Total number of trials) = 90 / 300.
Simplifying the fraction: 90/300 = 9/30 = 3/10.
6A survey was conducted on 200 students to find their favourite sport. The results are: Sport | Cricket | Football | Badminton | Basketball | Tennis ------|---------|----------|-----------|------------|-------- Number of Students | 80 | 50 | 30 | 25 | 15 What is the experimental probability that a randomly chosen student likes Badminton?
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Answer: A) 3/20
Hint: Identify the number of students who prefer Badminton and divide it by the total number of students surveyed.
Solution:
The total number of students surveyed (total trials) is 200.
The number of students who like Badminton (favourable outcomes) is 30.
Experimental probability P(likes Badminton) = (Number of students who like Badminton) / (Total number of students).
P(likes Badminton) = 30 / 200 = 3 / 20.
7A student, Ravi, performed an experiment where he drew a card from a deck 50 times, replacing it each time. He found that a red card was drawn 35 times. He calculated the probability of drawing a red card as 7/10. His friend, Priya, said he made a mistake and the probability should be 1. Why might Priya think Ravi made a mistake?
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Answer: D) Priya is incorrect; Ravi's calculation is correct based on the experimental data.
Hint: Focus on the definition of experimental probability and how it is derived from observed data, not from theoretical assumptions about the setup.
Solution:
Experimental probability is calculated directly from the results of an actual experiment, not from theoretical expectations.
Ravi conducted 50 trials, and the event 'drawing a red card' occurred 35 times.
His calculation for the experimental probability P(Red card) = (Number of red cards drawn) / (Total trials) = 35 / 50 = 7 / 10 is correct based on his experimental data.
Priya's claim that the probability should be 1 is incorrect, as a probability of 1 signifies a certain event, which drawing a red card is not. Option C refers to theoretical probability, which is not the focus when calculating experimental probability.
8Two events, A and B, were observed in an experiment with 100 trials. Event A occurred 45 times, and Event B occurred 60 times. Which of the following statements is true?
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Answer: B) Event B is more likely to occur than Event A.
Hint: Calculate the experimental probability for each event and then compare the numerical values to determine which is higher.
Solution:
The total number of trials for both events is 100.
For Event A: Number of occurrences = 45. Experimental probability P(A) = 45 / 100 = 0.45.
For Event B: Number of occurrences = 60. Experimental probability P(B) = 60 / 100 = 0.60.
Comparing the probabilities: 0.60 is greater than 0.45.
Therefore, Event B has a higher experimental probability and is more likely to occur than Event A.
9In an experiment, an event E occurred 60 times out of 250 trials. The experimental probability of event E is ______.
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Answer: A) 6/25
Hint: Apply the fundamental definition of experimental probability: (number of times the event occurred) / (total number of trials). Remember to simplify the fraction.
Solution:
The total number of trials in the experiment is 250.
The number of times event E occurred is 60.
The experimental probability P(E) = (Number of times E occurred) / (Total number of trials).
P(E) = 60 / 250.
Simplifying the fraction by dividing both numerator and denominator by their greatest common divisor (10): 60/250 = 6/25.
10Which of the following describes an impossible event in the context of rolling a standard six-sided die once?
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Answer: B) Getting a number greater than 6.
Hint: An impossible event is one that cannot happen under any circumstances during the experiment.
Solution:
A standard six-sided die has faces numbered 1, 2, 3, 4, 5, 6.
A) Getting an even number (2, 4, 6) is possible.
B) Getting a number greater than 6 is impossible, as the highest number on a standard die is 6. There are no outcomes for this event.
C) Getting a number less than 7 (1, 2, 3, 4, 5, 6) is a certain event, as all possible outcomes satisfy this condition.
D) Getting an odd number (1, 3, 5) is possible.
An impossible event has a probability of 0.
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Tips for Probability (संभाव्यता) 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 (संभाव्यता) MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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