A coin is tossed 16 times. What is the probability

Amiya Arellano

Amiya Arellano

Answered question

2022-02-11

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

Answer & Explanation

Rachel Frazier

Rachel Frazier

Beginner2022-02-12Added 14 answers

Step 1
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(=22)
possible results, thrice we have
8(=23)
possible results, etc. It works out to be, for 16 tosses:
216=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:
Cn, k=n!(k!)(nk)!
with n=population, k=picks
C16, 14=16!(14!)(1614)!=16!2!×14!=16×15×14!2×14!=120
And so we have:
P(14 heads in 16 tosses of a fair coin)=12065536=0.18%

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