# NCERT Class 12-Mathematics: Chapter – 13 Probability Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 .

**Answer**:

Let

Also,

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

## Long Answer (L. A.)

**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?

**Answer**:

(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

**Answer**:

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.

**Answer**:

(i)

(ii)

(iii)