Multiple choice

$(A)$ There are $30$ cards numbered from $1$ to $30$. One card is drawn at random. Find the probability that the number of the selected card is not divisible by $3$. $(B)$ A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers $1,2,3,4,5,6,7,8$ and these are equally likely outcomes. What is the probability that it will point at $(i)$ $8$ $(ii)$ An odd number $(iii)$ A number greater than $2$ $(iv)$ A number less than $9$

  1. $(A)\quad \displaystyle\frac{1}{3}\\(B)\space (i)\quad \displaystyle\frac{1}{8}\\ (ii)\quad \displaystyle\frac{1}{2}\\ (iii)\quad \displaystyle\frac{1}{4} \\ (iv)\quad 1$
  2. $(A)\quad \displaystyle\frac{1}{3}\\(B)\space (i)\quad \displaystyle\frac{10}{19}\\ (ii)\quad \displaystyle\frac{1}{2}\\ (iii)\quad \displaystyle\frac{3}{4} \\ (iv)\quad 1$
  3. $(A)\quad \displaystyle\frac{2}{3}\\(B)\space (i)\quad \displaystyle\frac{11}{16}\\ (ii)\quad \displaystyle\frac{1}{2}\\ (iii)\quad \displaystyle\frac{1}{4} \\ (iv)\quad 1$

  4. None of these
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D Correct answer
AI explanation

For part A, there are 10 multiples of 3 between 1 and 30, so the probability of a number not being divisible by 3 is 20 divided by 30, or 2 divided by 3. For part B, the probability of landing on 8 is 1 divided by 8. The probability of an odd number is 4 divided by 8, or 1 divided by 2. The probability of a number greater than 2 is 6 divided by 8, or 3 divided by 4. The probability of a number less than 9 is 1. None of the provided options contain these exact combinations of correct fractions, making none of these the correct choice.

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