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A random variable X has the following probability distribution : `{:(X:,1,2,3,4,5,6,7,8),(P(X):,0.15,0.23,0.12,0.10,0.20,0.08,0.07,0.08):}` for the ev

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A random variable X has the following probability distribution : X: 1 2 3 4 5 6 7 8 P(X): 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.08 for the events E=[X is a prime number] F={X<4}, the probability P(EOP), is. A. 0.50 B. 0.77 C. 0.35 D. 0.87 Select the correct answer from above options

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Correct Answer - B We have P(E)=P(X=2or,X=3or,X=3or,X=5or,X=7) =P(X=2)+P(X=3)+P(X=5)+P(X=7) =0.23+0.12+0.20+0.07=0.62 . P(F)=P(X<4) =P(X=1)+P(X=2)+P(X=3) =0.15+0.12+0.12=0.50 . P(E∩F)=P (X is a prime number less than 4) =P(X=2)+P(X=3)=0.23+0.12=0.35 ∴P(E∪F)=P(E)+P(E)+P(F)-P(E∩F) =0.62+0.50-0.35=0.77

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