Question 4 of 55beginner💡 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

According to the textbook, 'The probability of an event E is a number P(E) such that 0 ≤\leq P(E) ≤\leq 1.' This means the probability of any event must lie between 0 and 1, inclusive. Option (B) is -1.5, which is a negative number less than 0. Since probability cannot be negative, -1.5 cannot be the probability of an event. Options (A) 2/3, (C) 15% (which equals 0.15), and (D) 0.7 all lie within the valid range of 0 to 1.

Solution Steps

  1. Step 1: Recall the property that probability of an event satisfies 0 ≤\leq P(E) ≤\leq 1.

  2. Step 2: Check each option: (A) 2/3 ≈\approx 0.67, which lies between 0 and 1.

  3. Step 3: Check (B) -1.5, which is negative and less than 0.

  4. Step 4: Check (C) 15% = 0.15, which lies between 0 and 1.

  5. Step 5: Check (D) 0.7, which lies between 0 and 1.

  6. Step 6: Conclude that only option (B) violates the condition 0 ≤\leq P(E) ≤\leq 1.

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