# NCERT Class 12-Mathematics: Chapter –13 Probability Part 7

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Question 8:

Three events A, B and C have probabilities respectively. Given that , find the values of and .

Here,

And

Question 9:

Let and be two independent events such that and . Describe in words of the events whose probabilities are:

(i)

(ii)

(iii)

(iv)

(i) and occur

(ii) does not occur, but occurs

(iii) Either or , or both and occurs

(iv) Either or occurs, but not both

Question 10:

A discrete random variable X has the probability distribution given as below:

(i) Find the value of

(ii) Determine the mean of the distribution.

We have

(i) we know that,

(ii) Mean of the distribution

Question 11:

Prove that

(i)

(ii)

(i)

Hence proved.

(ii)

Hence proved.

Question 12:

If X is the number of tails in three tosses of a coin, determine the standard deviation of X.