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    Subject

    Quantitative Aptitude

    Topic

    Probability

    A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?

    ক)
    136/345
    খ)
    17/87
    গ)
    316/435
    ঘ)
    158/435

    Explanation

    n(s)=30C2n\left(s\right)={}^{30}C_2 Let A be the event of getting two oranges and B be the event of getting two non-defective fruits. and (A∩B)\left(A\cap B\right) be the event of getting two non-defective oranges ∴  P(A)=20C230C2,  P(B)=22C230C2  and  P(A∩B)=15C230C2\therefore\;P\left(A\right)=\frac{{}^{20}C_2}{{}^{30}C_2},\;P\left(B\right)=\frac{{}^{22}C_2}{{}^{30}C_2}\;and\;P\left(A\cap B\right)=\frac{{}^{15}C_2}{{}^{30}C_2} ∴P(A∪B)=P(A)+P(B)−P(A∩B)\therefore P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) = 20C230C2+22C230C2−15C230C2=316435\frac{{}^{20}C_2}{{}^{30}C_2}+\frac{{}^{22}C_2}{{}^{30}C_2}-\frac{{}^{15}C_2}{{}^{30}C_2}=\frac{316}{435}

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