Subject

    Quantitative Aptitude

    Topic

    Probability

    A fair coin is tossed 11 times. What is the probability that only the first two tosses will yield heads ?

    ক)
    (1/2)11
    খ)
    (9)(1/2)
    গ)
    (11C2)(1/2)9
    ঘ)
    (1/2)

    Explanation

    Probability of occurrence of an event, P(E) = Number of favorable outcomes/Numeber of possible outcomes = n(E)/n(S) ⇒ Probability of getting head in one coin = ½, ⇒ Probability of not getting head in one coin = 1- ½ = ½, Hence, All the 11 tosses are independent of each other. ∴ Required probability of getting only 2 times heads = (12)2×(12)9=(12)11\left(\frac12\right)^2\times\left(\frac12\right)^9=\left(\frac12\right)^{11}

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