A spinner is divided into 8 equal sectors numbered 1 to 8, and the pointer is equally likely to stop on any sector. It is spun once. Consider the following statements:
I. The probability that the pointer stops on a prime number is \(\frac{1}{2}\).
II. The probability that the pointer stops on a multiple of 3 is \(\frac{1}{3}\).
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only I
The spinner has 8 equally likely outcomes: 1 to 8. Probability = favourable outcomes \(\div\) 8.
Statement I — Correct.
Prime numbers from 1 to 8: 2, 3, 5, 7 (1 is not prime) → 4 outcomes
Probability \(=\frac{4}{8}=\frac{1}{2}\)
Statement II — Incorrect.
Multiples of 3 from 1 to 8: 3, 6 → 2 outcomes
Probability \(=\frac{2}{8}=\frac{1}{4}\), not \(\frac{1}{3}\)
Only statement I is correct.