Answer to Question #113218 in Statistics and Probability for Najah Ahmad

Question

A ball is drawn at random from a box containing 10 red balls, 30 white balls, 20 blue balls and 15 black balls.Obtain the probability that the ball drawn is:
(1)black or red
(2) not red or blue
(3)not blue
(4) white
(5) red, white,blue

Answer 1

The total number of ball in the box , $n(s)=10+30+20+15=75$ .

Let, red ball denoted by $R$

White ball denoted by $W$

Blue ball denoted by $B$

Black ball denoted by $Bl$ .

1) $P(R \ or Bl)=P(B)+P(Bl)$

$=\frac{10}{75}+\frac{15}{75}=\frac{25}{75}=\frac{1}{3}$

2) Let not red is denoted by $\sim R$ .

$P(\sim R \ or B)=P(\sim R \ \cup B)=P(\sim R)+P(B)-P(\sim R\ \cap B)$

$=1-P(R)+P(B)-P(B)$ [since $B\sub\ ( \sim R)$ ]

$=1-\frac{10}{75}=\frac{65}{75}=\frac{13}{15}$ .

3) $P(not \ B)=1-P(B)$

$=1-\frac{20}{75}=\frac{55}{75}=\frac{11}{15}$ .

4) $P(W)=\frac{30}{75}=\frac{2}{5}$

5) $P( R \ \cup W\ \cup \ B)=P(R)+P(W)+P(B)$

(As R,W,B are disjoint)

$=\frac{10}{75}+\frac{30}{75}+\frac{20}{75}=\frac{60}{75}=\frac{4}{5}$ .