A random variable X has the probability distributionX = x :12345678P(X) :0.150.230.120.10.20.080.070.05Events E = {X is a prime number} and F= {X / X

Engineering

Mathematics

Conditional Probability

Question

A random variable X has the probability distribution

X = x :	1	2	3	4	5	6	7	8
P(X) :	0.15	0.23	0.12	0.1	0.2	0.08	0.07	0.05

Events E = {X is a prime number} and F= {X / X < 4}

$(i) : \bar{(E \cup F)} = 0.23$

$(ii) : p (E \cup F) = 0.65$
Which of I, II is (are) true ?

I only

II only

both I and II

neither I nor II

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Prime numbers = 2, 3, 5, 7
F = 1, 2, 3
E∪F = {1, 2, 3, 5, 7}

$E \cup F = {1, 4, 5, 6, 7, 8}$

$\bar{P (E \cup F)} = 1 - P (E \cup F) = 0.1 + 0.08 + 0.05 = 0.23$

$P (E \cup F) = 1 - 0.23 - 0.12 = 0.65$
Hence, option 'C' is correct.

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