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JEE Main & Advanced Mathematics Probability Question Bank Odds in favour and odds against Addition theorem on probability

  • question_answer
    A random variable X has the 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 0.05
                For the events \[E=\{X\]is prime number} and \[F=\{X<4\}\], the probability of \[P(E\cup F)\] is                                           [AIEEE  2004]

    A)                 0.50       

    B)                 0.77

    C)                 0.35       

    D)                 0.87

    Correct Answer: B

    Solution :

                       \[E=\{x\] is a prime number}                    \[P(E)=P(2)+P(3)+P(5)+P(7)=0.62,\,\]                    \[F=\{x<4\}\], \[P(F)=P(1)+P(2)+P(3)=0.50\]                    and \[P(E\cap F)=P(2)+P(3)=0.35\]                    \[\therefore \] \[P(E\cup F)=P(E)+P(F)-P(E\cap F)\]                                                        = 0.62+0.50 ? 0.35 = 0.77.


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