A fair (unbiased) coin is tossed 15 times. The probability of getting exactly 8 Heads (round off to three decimal places), is ________.Correct answer is '0.196'. Can you explain this answer?

Question

Answer

Problem:
A fair (unbiased) coin is tossed 15 times. The probability of getting exactly 8 Heads (round off to three decimal places) is ________.

Solution:

To find the probability of getting exactly 8 Heads when a fair coin is tossed 15 times, we need to use the binomial probability formula. The binomial probability formula is given by:

P(x) = C(n, x) * p^x * q^(n-x)

Where:
P(x) = Probability of getting exactly x successes
C(n, x) = Combination of n items taken x at a time
p = Probability of getting a success in a single trial
q = Probability of getting a failure in a single trial
n = Total number of trials

In this case, the probability of getting a Head (success) in a single trial is 0.5, as the coin is fair. Therefore, p = 0.5. Similarly, the probability of getting a Tail (failure) in a single trial is also 0.5, so q = 0.5. The total number of trials is 15, so n = 15.

Now, we can substitute these values into the formula:

P(8) = C(15, 8) * 0.5^8 * 0.5^(15-8)

Calculating the Combination:
C(15, 8) = 15! / (8! * (15-8)!) = 3003

Calculating the Probability:
P(8) = 3003 * 0.5^8 * 0.5^7 = 3003 * 0.5^15

Rounding off the Probability:
P(8) = 3003 * 0.000030517578125 ≈ 0.091

Therefore, the probability of getting exactly 8 Heads when a fair coin is tossed 15 times is approximately 0.091.

Similar GATE Doubts

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?

Xis a random variable with uniform probability density function in the interval [-2,10], For Y = 2X- 6, the conditional probability P(Y< 7 I X > 5) (rounded off to three decimal places) is ____ . Correct answer is '0.3'. Can you explain this answer?

The probability that a 50 year flood may NOT occur at all during 25 years life of a project (round off to two decimal places), is _______. Correct answer is '0.60'. Can you explain this answer?

Top Courses for GATE

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Other Engg Branches

Related Exams

Company