# NCERT Class 12-Mathematics: Chapter – 13 Probability Part 10

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**Question 30**:

Two probability distributions of the discrete random variable X and Y are given below.

Prove .

**Answer**:

Since, we have to prove that,

From Eq. (i) and (ii) ,

Hence proved.

**Question 31**:

A factory produces bulbs. The probability that any one bulb is defective is and they are packed in boxes of 10. From a single box, find the probability that

(i) None of the bulbs is defective

(ii) Exactly two bulbs are defective

(iii) More than 8 bulbs work properly

**Answer**:

(i)

(ii)

(iii)

**Question 32**:

Suppose you have two coins which appear identical in your pocket. You know that one is fair and one is 2-headed. If you take one out, toss it and get a head, what is the probability that it was a fair coin?

**Answer**:

Let Event that a fair coin is drawn

Event that two headed coin is drawn

Event that tossed coin get a head

Now using Baye՚s theorem

**Question 33**:

Suppose that of the people with blood group O are left handed and of those with other blood groups are left handed of the people have blood group O. If a left handed person is selected at random, what is the probability that he/she will have blood group O?

**Answer**:

Blood group ‘O’ | Other than blood group ‘O’ | |

I. Number of people II. Percentage of left handed people |

By using Baye՚s theorem,

**Question 34**:

Two natural numbers are drawn one at a time, without replacement from the set . Find where .

**Answer**: