If you flip a fair coin 10 times, what is

Damian Kerr

Damian Kerr

Answered question

2022-02-12

If you flip a fair coin 10 times, what is the probability that it lands on heads exactly 4 times?

Answer & Explanation

Biscatta9rz

Biscatta9rz

Beginner2022-02-13Added 14 answers

The probability of getting a head in a single toss
p=12
The probability of not getting a head in a single toss
q=112=12
Now, using Binomial theorem of probability,
The probability of getting exactly r=4 heads in total n=10 tosses
=10C4(12)4(12)104
=10×9×8×74!124126
=2493524(210)
=10529
iluvyou23452nwj

iluvyou23452nwj

Beginner2022-02-14Added 19 answers

Answer: The probability is approximately 20.51%.
This question uses the binomial distribution.
Let X be the number of heads in 10 tosses.
Then X is distributed as B(n=10,p=12).
The probability of X being 4 is therefore
P(X=4)=10C4(12)4(112)104
=210(116)(12)6
=210(116)(164)
=2101024=1055120.2051

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