# NCERT Class 12-Mathematics: Chapter –13 Probability Part 12

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Question 40:

An urn contains white and black balls. A ball is drawn at random and is put back into the urn along with additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on .

Let

Also,

Hence, the probability of drawing a whit ball does not depend on k.

Question 41:

Three bags contain a number of red and white balls as follows:

Bag red balls, Bag red balls and 1 white ball

Bag white balls.

The probability that bag i will be chosen and a ball is selected from it is

. What is the probability that

(i) A red ball will be selected? (ii) A white ball is selected?

(i)

(ii)

Question 42:

Refer to Question above. If a white ball is selected, what is the probability that it came from

(i) Bag 2 (ii) Bag 3

Referring to the above solution, using Baye’s theorem, we have

(ii)

Question 43:

A shopkeeper sells three types of flower seeds and . They are sold as a mixture where the proportions are respectively. The germination rates of the three types of seeds are , and . Calculate the probability

(i) Of a randomly chosen seed to germinate

(ii) That it will not germinate given that the seed is of type ,

(iii) That it is of the type given that a randomly chosen seed does not germinate.