Answer to Question #270722 in Statistics and Probability for Abs

Question

An individual is handover a bag filled with balls of different colours.the probability of a randomly chosen red ball is 0.2, yellow ball is 0.2, green ball is 0.1,orange ball is 0.1,blue ball is 0.3 and white ball is 0.1.

If a ball is drawn at random from the bag, what is the probability of each of that

I. It is either Blue or Red in colour.

II. It is notYellow in colour.

III. It is neither Orange nor White in colour.

IV. It is either Blue or Red or Yellow or Green or Orange or White

Answer 1

Define the following events.

Let $R,Y,G,O,B,W$ be the events for randomly choosing red, yellow, green, orange, blue and white balls respectively then, the probabilities for randomly selecting any of the balls are given below.

$p(R)=0.2, \space p(Y)=0.2,\space p(G)=0.1,\space p(O)=0.1,\space p(B)=0.3,\space p(W)=0.1$

a.

The probability of selecting a blue or red ball is given as,

p(B or R)=p(B)+p(R)=0.3+0.2=0.5

Therefore, the probability of selecting a blue or red ball is 0.5

b.

The probability that the randomly selected ball is not yellow is given as,

$p(Y')=1-p(Y)=1-0.2=0.8$

Therefore, the probability that the ball selected is not yellow in color is 0.8.

c.

The probability that the ball selected is neither orange nor white is,

p(O' or W')=1-p(O or W).

Now,

p(O or W)=0.1+0.1=0.2

Therefore, p(~O or ~W)=1-0.2=0.8

Thus, the probability that the ball selected is neither orange nor white is 0.8.

d.

 The probability that the selected ball is either Blue or Red or Yellow or Green or Orange or White is,

p(B or R or Y or G or O or W)=p(B)+p(R)+p(G)+p(O)+p(Y)+p(W)=0.2+0.2+0.1+0.1+0.3+0.1=1

Thus, the probability that the randomly selected ball is either Blue or Red or Yellow or Green or Orange or White is 1.