Question:
From the following laws of probability, which are true ?
A. If probability of occurrence of an event is 1, the event will occur certainly.
B. If probability of occurrence of an event is 0, the event will never occur.
C. The probability of any event must assume a value between 0 and 1.
D. Closer the probability is to 1, the more likely it is that event will not occur.
E. Closer the probability is to 0, the more likely it is that event will occur.
Choose the correct answer from the options given below :
From the following laws of probability, which are true ?
A. If probability of occurrence of an event is 1, the event will occur certainly.
B. If probability of occurrence of an event is 0, the event will never occur.
C. The probability of any event must assume a value between 0 and 1.
D. Closer the probability is to 1, the more likely it is that event will not occur.
E. Closer the probability is to 0, the more likely it is that event will occur.
Choose the correct answer from the options given below :
A. If probability of occurrence of an event is 1, the event will occur certainly.
B. If probability of occurrence of an event is 0, the event will never occur.
C. The probability of any event must assume a value between 0 and 1.
D. Closer the probability is to 1, the more likely it is that event will not occur.
E. Closer the probability is to 0, the more likely it is that event will occur.
Choose the correct answer from the options given below :
Show Hint
Probability acts exactly like a percentage divided by 100. $0 = 0\%$, $0.5 = 50\%$, and $1 = 100\%$. The higher the number, the more likely it happens!
Updated On: Jul 31, 2026
- A, B, C only
- A, C, D only
- B, C, E only
- B, E only
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Concept:
This question tests the fundamental, axiomatic rules of probability theory, which are mathematically established foundations for all statistical analysis.
Step 2: Step-by-step Explanation:
• Probability ($P$) is a mathematical measure of the likelihood that a specific event will occur.
• Statement C is True: According to Kolmogorov's First Axiom of probability, the probability of any event $E$ is a real number bounded exactly between zero and one (inclusive). Expressed mathematically: $0 \leq P(E) \leq 1$.
• Statement A is True: If $P(E) = 1$, the event is considered an "absolute certainty" or a "sure event." It is guaranteed to happen 100% of the time.
• Statement B is True: If $P(E) = 0$, the event is considered an "impossible event." There is a 0% chance of it occurring, meaning it will never happen.
• Statement D is False: The closer a probability moves toward 1, the more likely the event is to occur, not less likely.
• Statement E is False: The closer a probability moves toward 0, the less likely the event is to occur, not more likely.
• Therefore, only statements A, B, and C represent valid mathematical laws of probability.
Step 3: Final Answer:
The correct options are A, B, and C only.
This question tests the fundamental, axiomatic rules of probability theory, which are mathematically established foundations for all statistical analysis.
Step 2: Step-by-step Explanation:
• Probability ($P$) is a mathematical measure of the likelihood that a specific event will occur.
• Statement C is True: According to Kolmogorov's First Axiom of probability, the probability of any event $E$ is a real number bounded exactly between zero and one (inclusive). Expressed mathematically: $0 \leq P(E) \leq 1$.
• Statement A is True: If $P(E) = 1$, the event is considered an "absolute certainty" or a "sure event." It is guaranteed to happen 100% of the time.
• Statement B is True: If $P(E) = 0$, the event is considered an "impossible event." There is a 0% chance of it occurring, meaning it will never happen.
• Statement D is False: The closer a probability moves toward 1, the more likely the event is to occur, not less likely.
• Statement E is False: The closer a probability moves toward 0, the less likely the event is to occur, not more likely.
• Therefore, only statements A, B, and C represent valid mathematical laws of probability.
Step 3: Final Answer:
The correct options are A, B, and C only.
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