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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]
First 10 times probability that head will appear exactly 4 times
P [4 heads in 10 tosses] ⋅ P [4 tails in 10 tosses]
Most Upvoted Answer
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.
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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