# NCERT Class 12-Mathematics: Chapter –13 Probability Part 14

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**Question 48:**

An item is manufactured by three machines A, B and C. Out of the total number of items manufactured during a specified period, are manufactured on A, on B and on . of the items produced on A and of items produced on B are defective, and of these produced on C are defective. All the items are stored at one godown. One item is drawn at random and is found to be defective. What is the probability that it was manufactured on machine A?

**Answer:**

Let

Let E be the event that an item is defective.

**Question 49:**

Let X be a discrete random variable whose probability distribution is defined as follows:

where is a constant. Calculate

(i) The value of

(ii)

(iii) Standard deviation of .

**Answer:**

(i)

(ii)

(iii)

**Question 50:**

The probability distribution of a discrete random variable is given as under:

Calculate:

(i) The value of A if

(ii) Variance of .

**Answer:**

(i) We have,

Since,

(ii) We know that