Find at Least Three Heads?

Seven unbiased coins are tossed 128 times. In how many throws would you find at least three heads?

  1. 99
  2. 102
  3. 103
  4. 104
Anurag Mishra Professor Asked on 3rd October 2015 in Maths.
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  • 1 Answer(s)

    Answer: (1) 99

    Explanation:-
    Let the number of heads obtained in a throw of 7 coins = X

    Then,  X =  B(n = 7, p = 12)

    The probability mass function is p(x) = 7Cx (12)x (12)7 – x x = 0, 1, 2,…….,7

    P(at least 3 heads) = 1 – P(at most 2 heads)

    = 1- {p(0) + p(1) + p(2)}

    = 1- {7C0 (1/2)7 + 7C1 (1/2)7 + 7C2(1/2)7 } = 99/128

    The number of tosses resulting in at least 3 heads = n XP(at least 3 heads)

    = 128 × 99/128 = 99

    Then,  in 99 tosses we expect at least 3 heads to occur.

    Hence, the answer is (1) 99.

    Anurag Mishra Professor Answered on 4th October 2015.
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