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  • Question
  • A fair coin is tossed 100 times, The probability of getting head an odd number of times is?


  • Options
  • A. 1/4
  • B. 2/3
  • C. 1/2
  • D. 3/4

  • Correct Answer
  • 1/2 

    Explanation

    n(S) = 2100
    n(E) = No. of favourable ways = 100C1 + 100C3 + ... 100 C99 = 2100-1 = 299
    [? nC1 + nC3 + nC5 + ........................... = 2n-1 ]
    ? P(E)= n(E)/n(S) = 299/2100 = 1/2

    Note : The given case can be generalised as "If a unbiased coin is tossed 'n' times, then the chance that the head will present itself an odd number of times is 1/2. "


  • Probability problems


    Search Results


    • 1. 
      All the boys are sitting together.

    • Options
    • A. 3/42
    • B. 41/42
    • C. 3/35
    • D. 1/42
    • Discuss
    • 2. 
      All the girls are sitting together.

    • Options
    • A. 1/42
    • B. 41/42
    • C. 3/35
    • D. 1/42
    • Discuss
    • 3. 
      All the boys are not sitting together?

    • Options
    • A. 3/35
    • B. 43/49
    • C. 41/42
    • D. 1/42
    • Discuss
    • 4. 
      All the girls are not sitting together?

    • Options
    • A. 41/42
    • B. 39/42
    • C. 31/42
    • D. 31/35
    • Discuss
    • 5. 
      If three marbles are picked at random, what is the probability that either all are green or all are red?

    • Options
    • A. 7/44
    • B. 7/12
    • C. 5/12
    • D. 1/44
    • Discuss
    • 6. 
      Out of 15 students studying in a class, 7 are from Maharastra, 5 are from Karnataka and 3 are from Goa, Four students are to be selected at random. What are the chances that at least one is from Karnataka?

    • Options
    • A. 12/13
    • B. 11/13
    • C. 10/15
    • D. 1/15
    • Discuss
    • 7. 
      In a box carrying one dozen of oranges, one third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one oranges out of the three oranges picked up is good?

    • Options
    • A. 1/55
    • B. 54/55
    • C. 45/55
    • D. 3/55
    • Discuss
    • 8. 
      What is the probability that a leap year selected randomly will have 53 Mondays?

    • Options
    • A. 2/7
    • B. 5/7
    • C. 1/7
    • D. Data inadequate
    • Discuss
    • 9. 
      What is the probability that a leap year selected randomly will have 53 Mondays?

    • Options
    • A. 2/7
    • B. 5/7
    • C. 1/7
    • D. Data inadequate
    • Discuss
    • 10. 
      If the probability for A fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is?

    • Options
    • A. 0.38
    • B. 0.44
    • C. 0.50
    • D. 0.94
    • Discuss


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