SUMMARY: This chapter introduces the concept of probability, focusing on the theoretical approach to understanding and calculating the likelihood of events. KEY TOPICS: probability of an event, experimental probability, theoretical probability, complementary events, probability of equally likely outcomes, probability of impossible and certain events, sample space, event, outcomes, probability formula
What is the probability of rolling a sum of 7 with two six-sided dice?
A1/6
B1/12
C1/36
D1/3
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Correct answer: Option 1 — 1/6
Q21 Mark
If a coin is tossed, what is the probability of getting tails?
A1/4
B1/2
C1/3
D1
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Correct answer: Option 2 — 1/2
Q31 Mark
In a bag containing 3 red, 2 blue, and 5 green balls, what is the probability of drawing a blue ball?
A1/5
B1/10
C2/10
D1/2
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Correct answer: Option 3 — 2/10
Q41 Mark
If the probability of an event A is 0.7, what is the probability of the complementary event A'?
A0.3
B0.7
C1.0
D0.5
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Correct answer: Option 1 — 0.3
Q51 Mark
A box contains 4 white, 3 black, and 2 red balls. If one ball is drawn at random, what is the probability that it is neither white nor red?
A1/3
B1/2
C2/9
D1/4
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Correct answer: Option 2 — 1/2
Short Answer Questions5 questions
Q63 Marks
Define the term 'sample space' in probability. Provide an example.
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The sample space is the set of all possible outcomes of a probability experiment. For example, when tossing a coin, the sample space is {Heads, Tails}.
Q73 Marks
What is the probability of getting a number greater than 4 when rolling a fair six-sided die?
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The numbers greater than 4 on a six-sided die are 5 and 6. Therefore, the probability is 2 out of 6, which simplifies to 1/3.
Q83 Marks
Explain the concept of complementary events with an example.
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Complementary events are two outcomes of an event that cover all possible outcomes. For instance, if event A is 'rolling a 3 on a die', then its complement, A', is 'not rolling a 3'.
Q93 Marks
Calculate the theoretical probability of drawing an ace from a standard deck of 52 playing cards.
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There are 4 aces in a standard deck of 52 cards. The theoretical probability of drawing an ace is 4/52, which simplifies to 1/13.
Q103 Marks
If an event has a probability of 0, what does that indicate about the event? Provide an example.
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A probability of 0 indicates that the event is impossible and cannot occur. For example, the probability of rolling a 7 on a standard six-sided die is 0, as it is not a possible outcome.
Long Answer Questions5 questions
Q116 Marks
Define the concept of probability and explain the difference between theoretical probability and experimental probability. Provide an example for each type of probability to illustrate your explanation.
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Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. Theoretical probability is calculated based on the possible outcomes in a perfect scenario, while experimental probability is derived from actual experiments or trials. For example, if a fair die is rolled, the theoretical probability of rolling a 3 is 1/6, as there is one favorable outcome out of six possible outcomes. In contrast, if a die is rolled 60 times and a 3 appears 10 times, the experimental probability of rolling a 3 would be 10/60 or 1/6, which aligns with the theoretical probability.
Q126 Marks
Explain the concept of complementary events in probability. How do you calculate the probability of an event and its complement? Provide a detailed example to support your explanation.
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Complementary events are pairs of events where one event occurs if and only if the other does not. The probability of an event A and its complement A' (not A) must sum to 1, i.e., P(A) + P(A') = 1. For instance, if the probability of raining tomorrow (event A) is 0.3, then the probability of it not raining (event A') is 1 - 0.3 = 0.7. This relationship helps in calculating probabilities efficiently, as knowing one can help determine the other.
Q136 Marks
A bag contains 3 red, 5 blue, and 2 green balls. If one ball is drawn at random, calculate the probability of drawing a blue ball. Additionally, determine the probability of drawing a ball that is not red. Explain your calculations step by step.
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To find the probability of drawing a blue ball, first, determine the total number of balls in the bag, which is 3 (red) + 5 (blue) + 2 (green) = 10 balls. The probability of drawing a blue ball is the number of blue balls divided by the total number of balls, P(blue) = 5/10 = 1/2. To find the probability of drawing a ball that is not red, we can either calculate the probability of drawing a red ball and subtract it from 1 or count the non-red balls directly. The number of non-red balls is 5 (blue) + 2 (green) = 7. Therefore, P(not red) = 7/10.
Q146 Marks
Discuss the concept of equally likely outcomes in probability. How does this concept help in calculating the probability of an event? Illustrate your answer with an example involving a coin toss.
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Equally likely outcomes refer to situations where each outcome has the same chance of occurring. This concept simplifies the calculation of probability because the probability of an event can be determined by counting the number of favorable outcomes and dividing it by the total number of outcomes. For example, when tossing a fair coin, there are two equally likely outcomes: heads and tails. If we want to find the probability of getting heads, we count the favorable outcome (heads) which is 1, and divide it by the total outcomes (2), giving us P(heads) = 1/2. This method can be applied to various scenarios involving equally likely outcomes.
Q156 Marks
A class consists of 30 students, out of which 18 are boys and 12 are girls. If a student is selected at random, calculate the probability of selecting a girl. Furthermore, explain the implications of this probability in the context of gender distribution in the class.
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To calculate the probability of selecting a girl from the class, we first identify the total number of students, which is 30. The number of girls in the class is 12. Therefore, the probability of selecting a girl is P(girl) = number of girls / total number of students = 12/30 = 2/5. This probability indicates that there is a 40% chance of randomly selecting a girl from the class. This information can be useful for understanding the gender distribution within the class and can inform decisions related to group activities or discussions.
Assertion–Reason Questions5 questions
Q161 Mark
Assertion (A): The probability of getting a head in a fair coin toss is 0.5.
Reason (R): In a fair coin, there are two equally likely outcomes: heads and tails.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q171 Mark
Assertion (A): The probability of rolling a 7 on a standard six-sided die is 0.
Reason (R): A standard die has only six faces numbered from 1 to 6.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q181 Mark
Assertion (A): The sum of the probabilities of all possible outcomes of an event is always 1.
Reason (R): This is a fundamental property of probability.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q191 Mark
Assertion (A): If two events are complementary, the probability of one event occurring is equal to the probability of the other event not occurring.
Reason (R): Complementary events are defined as events that cannot happen at the same time.
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Correct answer: Option 2 —
Both A and R are true, but R is not the correct explanation of A.
Q201 Mark
Assertion (A): The experimental probability of an event can differ from its theoretical probability.
Reason (R): Experimental probability is based on actual experiments and may vary due to random chance.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Statement-Based Questions5 questions
Q211 Mark
Statement 1: The probability of an event is always a number between 0 and 1.
Statement 2: The probability of an impossible event is 1.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q221 Mark
Statement 1: If two events are complementary, the sum of their probabilities is 1.
Statement 2: The sample space is the set of all possible outcomes of an experiment.
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Correct answer: Option 1 —
Both statements are true.
Q231 Mark
Statement 1: The theoretical probability of an event is calculated based on the actual outcomes of an experiment.
Statement 2: The probability of getting a head when tossing a fair coin is 0.5.
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Correct answer: Option 3 —
Only Statement 2 is true.
Q241 Mark
Statement 1: Experimental probability is based on the number of times an event occurs in a series of trials.
Statement 2: The probability of a certain event is 0.
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Correct answer: Option 4 —
Both statements are false.
Q251 Mark
Statement 1: If an event has a probability of 0.2, it is certain to occur.
Statement 2: The probability of equally likely outcomes can be calculated by dividing the number of favorable outcomes by the total number of outcomes.
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Correct answer: Option 3 —
Only Statement 2 is true.
