Question

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
$\left(i\right)$ Even
$\left(ii\right)$ A prime
$\left(iii\right)$ Divisible by $2$ and $3$ both.

• A. $\left(i\right)\frac{2}{15}\left(ii\right)\frac{1}{13}\left(iii\right)\frac{3}{11}$
• B. $\left(i\right)\frac{11}{18}\left(ii\right)\frac{9}{13}\left(iii\right)\frac{3}{19}$
• C. $\left(i\right)\frac{8}{17}\left(ii\right)\frac{7}{17}\left(iii\right)\frac{3}{17}$
• D. None of these
  

Answer 1

Answer: (C)

$\left(i\right)\frac{8}{17}\left(ii\right)\frac{7}{17}\left(iii\right)\frac{3}{17}$

Total cards bearing numbers 3 to 19 = 17
(i) Total no. of cards bearing even no. = 8
$\therefore$ favorable outcomes= 8
$\therefore$ probability = $\frac{8}{17}$
(ii) Prime no.'s from 3 to 19 are:
3,5,7,11,13,17,19
Total no. of cards bearing prime no. = 7
$\therefore$ favorable outcomes= 7
$\therefore$ probability = $\frac{7}{17}$
(iii) No's divisible by 2 and 3 both from 3 to 19 are:
6,12,18
Total no. of cards bearing no. divisible by 2 and 3 both = 3
$\therefore$ favorable outcomes= 3
$\therefore$ probability = $\frac{3}{17}$