Multiple choice

A box contains $20$ balls bearing numbers $1, 2, 3, ... , 20$ respectively. A ball is drawn at random from the box what is the probability that the number on the ball is $(i)$ An odd number $(ii)$ Divisible by $2$ or $3$ $(iii)$ A prime number $(iv)$ Not divisible by $10$

  1. $(i)\quad \displaystyle\frac{1}{3}\\ (ii)\quad \displaystyle\frac{12}{19}\\(iii)\quad \displaystyle\frac{2}{5}\\ (iv)\quad \displaystyle\frac{9}{10}$
  2. $(i)\quad \displaystyle\frac{1}{2}\\ (ii)\quad \displaystyle\frac{13}{20}\\(iii)\quad \displaystyle\frac{2}{5}\\ (iv)\quad \displaystyle\frac{9}{10}$
  3. $(i)\quad \displaystyle\frac{1}{3}\\ (ii)\quad \displaystyle\frac{18}{37}\\(iii)\quad \displaystyle\frac{2}{5}\\ (iv)\quad \displaystyle\frac{2}{5}$
  4. $(i)\quad \displaystyle\frac{1}{2}\\ (ii)\quad \displaystyle\frac{15}{29}\\(iii)\quad \displaystyle\frac{2}{5}\\ (iv)\quad \displaystyle\frac{2}{5}$
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B Correct answer
Explanation

For (i), odd numbers are 10 out of 20, so 1/2. For (ii), multiples of 2 (10) plus multiples of 3 (6) minus multiples of 6 (3) equals 13/20. For (iii), primes are 2, 3, 5, 7, 11, 13, 17, 19 (8 total), so 8/20 = 2/5. For (iv), numbers divisible by 10 are 10 and 20 (2 total), so 18/20 = 9/10.

AI explanation

The total number of outcomes is 20. Using the classical definition of probability, there are 10 odd numbers, so the probability of an odd number is 10/20 = 1/2. There are 13 numbers divisible by 2 or 3, making that probability 13/20. There are 8 prime numbers between 1 and 20, so the probability of a prime is 8/20 = 2/5. Finally, only two numbers are divisible by 10, meaning 18 are not, giving a probability of 18/20 = 9/10.

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