Question 4 of 22beginner💡 UnderstandMCQ1 mark

Which of the following cannot be the probability of an event?

Exercise: EXERCISE 14.1 | Q: 4 | (Page Page 13)
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Explanation

Option (B) is the correct answer because the probability of an event must always lie between 0 and 1, inclusive. The provided context explicitly states that for any event E, the probability P(E) satisfies the inequality 0 ≤\leq P(E) ≤\leq 1. Since -1.5 is a negative number (less than 0), it falls outside this permissible range and therefore cannot represent the probability of an event. Options (A), (C), and (D) are valid probabilities as 2/3 ≈\approx 0.67, 15% = 0.15, and 0.7 all lie within the range [0, 1].

Solution Steps

  1. Step 1: Identify the range of probability from the context: The probability of an event E is a number P(E) such that 0 ≤\leq P(E) ≤\leq 1.

  2. Step 2: Analyze Option (A): 2/3 is approximately 0.67. Since 0 ≤\leq 0.67 ≤\leq 1, it is a valid probability.

  3. Step 3: Analyze Option (B): -1.5 is less than 0. Since probability cannot be negative, it cannot be the probability of an event.

  4. Step 4: Analyze Option (C): 15% is equal to 15/100 or 0.15. Since 0 ≤\leq 0.15 ≤\leq 1, it is a valid probability.

  5. Step 5: Analyze Option (D): 0.7 lies between 0 and 1. Thus, it is a valid probability.

  6. Step 6: Conclude that -1.5 is the only value that violates the condition 0 ≤\leq P(E) ≤\leq 1.

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