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A fair coin is tossed 20 times. The probability that 'head' will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).
    Correct answer is '0.042'. Can you explain this answer?
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    A fair coin is tossed 20 times. The probability that head will appear ...
    Fair coin tossed 20 times
    First 10 times probability that head will appear exactly 4 times
    P [4 heads in 10 tosses] ⋅ P [4 tails in 10 tosses]
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    A fair coin is tossed 20 times. The probability that head will appear ...
    Tail will appear exactly 6 times in the last ten tosses can be calculated using the binomial distribution.

    The probability of getting exactly 4 heads in the first 10 tosses is given by:

    P(4 heads) = (10 choose 4) * (1/2)^4 * (1/2)^6 = 210 * 1/2^10

    Similarly, the probability of getting exactly 6 tails in the last 10 tosses is given by:

    P(6 tails) = (10 choose 6) * (1/2)^6 * (1/2)^4 = 210 * 1/2^10

    The probability of these two events occurring together is the product of their probabilities:

    P(4 heads and 6 tails) = P(4 heads) * P(6 tails) = (210 * 1/2^10) * (210 * 1/2^10) = 441/2^20

    Therefore, the probability that head will appear exactly 4 times in the first ten tosses, and tail will appear exactly 6 times in the last ten tosses is 441/2^20 or approximately 0.000840.
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    A fair coin is tossed 20 times. The probability that head will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).Correct answer is '0.042'. Can you explain this answer?
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    A fair coin is tossed 20 times. The probability that head will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).Correct answer is '0.042'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A fair coin is tossed 20 times. The probability that head will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).Correct answer is '0.042'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fair coin is tossed 20 times. The probability that head will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).Correct answer is '0.042'. Can you explain this answer?.
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