Question

A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is:
(i) a black ball
(ii) a red ball
(iii) a white ball
(iv) not a red ball
(v) not a black ball

Answer 1

In a bag, 3 balls are white
2 balls are red
5 balls are black
Total number of balls = 3+ 2+ 5= 10
(i) Number of possible outcome of one black ball = 10
and number of favourable outcome of one black ball= 5
$\therefore$ P(E) = $\frac{Numberoffavourableoutcome}{Numberofallpossibleoutcome}$
$=\frac{5}{10}=\frac{1}{2}$
(ii) Number of possible outcome of one red ball= 10
and number of favourable outcome= 2
$\therefore$ P(E)= $\frac{Numberoffavourableoutcome}{Numberofallpossibleoutcome}$
$=\frac{2}{10}=\frac{1}{5}$
(iii) Number of possible outcome of white ball= 10
and number of favourable outcome= 3
$\therefore$ P(E)= $\frac{Numberoffavourableoutcome}{Numberofallpossibleoutcome}$
$=\frac{3}{10}$
(iv) Number of possible outcome= 10
Number of favourable outcome= 3+5=8
not a red ball
$\therefore$ = $\frac{Numberoffavourableoutcome}{Numberofallpossibleoutcome}$
$=\frac{8}{10}=\frac{4}{5}$
(v) Number of possible outcomes=10
Number of favourable outcome
not a black ball= 3+2=5
$\therefore$ = $\frac{Numberoffavourableoutcome}{Numberofallpossibleoutcome}$
$=\frac{5}{10}=\frac{1}{2}$