# NCERT Class 12-Mathematics: Chapter – 13 Probability Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 6**:

Three machines in a certain factory produce and , respectively, of the total daily output of electric tubes. It is known that of the tubes produced one each of machines E1 and E2 are defective, and that of those produced on are defective. If one tube is picked up at random from a day՚s production, calculate the probability that it is defective.

**Answer**:

Let D be the event that the picked up tube is defective

Let and be the events that the tube is produced on machines and , respectively .

Putting these values in (1) , we get

**Question 7**:

Find the probability that in throws of a fair die a score which is a multiple of 3 will be obtained in at least 8 of the throws.

**Answer**:

Here success is a score which is a multiple of i.e.. , or .

Therefore,

The probability of successes in throws is given by

Now

**Question 8**:

A discrete random variable X has the following probability distribution:

Find the value of . Also find the mean of the distribution.

**Answer**:

Since we have

Therefore, the permissible value of

## Long Answer (L. A.)

**Question 9**:

Four balls are to be drawn without replacement from a box containing 8 red and 4 white balls. If X denotes the number of red ball drawn, find the probability distribution of X.

**Answer**:

Since 4 balls have to be drawn, therefore, X can take the values .

Thus the following is the required probability distribution of