Multiple choice

Cards bearing numbers $3$ to $19$ are put in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card drawn is $(i)$ Even $(ii)$ A prime $(iii)$ Divisible by $2$ and $3$ both.

  1. $(i)\quad \displaystyle\frac{2}{15}\\(ii)\quad \displaystyle\frac{1}{13}\\(iii)\quad \displaystyle\frac{3}{11}$
  2. $(i)\quad \displaystyle\frac{11}{18}\\(ii)\quad \displaystyle\frac{9}{13}\\(iii)\quad \displaystyle\frac{3}{19}$
  3. $(i)\quad \displaystyle\frac{8}{17}\\(ii)\quad \displaystyle\frac{7}{17}\\(iii)\quad \displaystyle\frac{3}{17}$

  4. None of these
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C Correct answer
Explanation

Numbers 3 to 19: count = 17. (i) Even: 4, 6, 8, 10, 12, 14, 16, 18 (8 numbers). Prob = 8/17. (ii) Prime: 3, 5, 7, 11, 13, 17, 19 (7 numbers). Prob = 7/17. (iii) Divisible by 2 and 3 (i.e., 6): 6, 12, 18 (3 numbers). Prob = 3/17.

AI explanation

The cards are numbered from 3 to 19, which gives a total of 17 possible outcomes. For an even number, there are 8 outcomes (4, 6, 8, 10, 12, 14, 16, 18), giving a probability of 8/17. For a prime number, there are 7 outcomes (3, 5, 7, 11, 13, 17, 19), making the probability 7/17. For a number divisible by both 2 and 3, the outcomes are 6, 12, and 18, which gives a probability of 3/17.

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