Mathematics Part-II

Book: Mathematics Part-II

Chapter: 13. Probability

Subject: Maths - Class 12th

Q. No. 15 of Exercise 13.4

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15

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var (X).

Given: X = 0 if members oppose, and X = 1 if members are in favour.

P(X = 0)


P(X = 1)


Hence, the required probability distribution is,


X



0



1



P(X)



0.3



0.7



Therefore E(X) is:



= 0 × 0.3 + 1 × 0.7


E(X) = 0.7


And E(X2) is:



= (0)2 × 0.3 + (1)2 × 0.7


E(X2) = 0.7


Then Variance, Var(X) = E(X2) – (E(X))2


= 0.7 – (0.7)2


= 0.7 – 0.49 = 0.21


15

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