Question

Fifteen cards numbered $1,2,3,4,...14,15$ are put in a box and mixed throughly. A man draws a card at random from the box. Find the probability that the number on the card is
$\left(i\right)$ An odd number
$\left(ii\right)$ A multiple of $4$
$\left(iii\right)$ Divisible by $5$
$\left(iv\right)$ Divisible by $2$ and $3$
$\left(v\right)$ Less than or equal to $10$

Answer 1

Since, total cards = 15
(i) total odd no.'s from 1 to 15 = 8
$\therefore$ favorable outcomes= 8
$\therefore$ probability = $\frac{8}{15}$
(ii) Total Multiples of 4 from 1 to 15 = 3
$\therefore$ favorable outcomes= 3
$\therefore$ probability = $\frac{3}{15}=\frac{1}{5}$
(iii) Total no's divisible by 5 from 1 to 15 = 3
$\therefore$ favorable outcomes= 3
$\therefore$ probability = $\frac{3}{15}=\frac{1}{5}$
(iv) Total no's divisible by 2 and 3 from 1 to 15 are:
6,12
$\therefore$ favorable outcomes= 2
$\therefore$ probability = $\frac{2}{15}$
(v) Total no's less than or equal to 10 from 1 to 15 = 10
$\therefore$ favorable outcomes= 10
$\therefore$ probability = $\frac{10}{15}=\frac{2}{3}$