A coin is tossed 16 times. What is the probability of obtaining exactly 14 heads?

Answer 1

#P("14 heads in 16 tosses of a fair coin")=120/65536~=0.18%#

When calculating a probability, we take the ratio of the number of ways to meet a certain condition (i.e. the numerator) divided by the number of ways to pick from a pool (i.e. the denominator).

So what are the number of ways the flip of a coin 16 times can come out? Each toss has two possible results - if we toss twice we have 4 #(=2^2)# possible results, thrice we have 8 #(=2^3)# possible results, etc. It works out to be, for 16 tosses:
#2^16=65,536#

Of those results, how many ways can we achieve 14 heads in 16 tosses?

This is a combinations calculation, with the general formula:

#C_(n,k)=(n!)/((k!)(n-k)!)# with #n="population", k="picks"#
#C_(16,14)=(16!)/((14!)(16-14)!)=(16!)/(2!xx14!)=(16xx15xx14!)/(2xx14!)=120#

And so we have:

#P("14 heads in 16 tosses of a fair coin")=120/65536~=0.18%#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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