Posted by **Sam** on Wednesday, March 21, 2012 at 7:55pm.

Suppose an unfair coin comes up heads 52.2% of the time if it is flipped. If the coin is flipped 26 times, what is the probability that:

a) it comes up tails exactly 12 times?

b) it comes up heads more than 22 times?

- probability -
**MathMate**, Wednesday, March 21, 2012 at 9:49pm
This is a binomial expansion with p=0.522, and q=1-p=0.478.

We will calculate the terms of

(p+q)^26.

Using the notation

(n,r)=n!/((n-r)!r!)=n choose r

the binomial expansion can be expressed as

(p+q)^26

=p^26+(26,1)p^25q+(26,2)p^24q^2+...+(26,r)p^(26-r)q^r...+(26,1)pq^25+(26,0)q^26

P(12 tails)

=P(14 heads)

=(26,12)p^(12)q^(14)

=0.1285...

P(>22)

=P(23)+P(24)+P(25)+P(26)

=(26,3)p^23q^3+(26,2)p^24q^2+(26,1)p^25q+(26,0)p^26

=0.00001759...

## Answer this Question

## Related Questions

- Probability - Suppose that an unfair coin comes up heads 54.1% of the time. The...
- statistics - air coin is flipped 20 times. a. Determine the probability that the...
- Statistics - Suppose Tori has an unfair coin which lands on Tails with ...
- MATH - an unfair coin with pr[tails]= .15 is flipped 6 times. what is the ...
- math - Carolyn tested a coin to see if it was evenly weighted. She flipped the ...
- Math - we have 2 coins: coin 1 comes up with the probability of tails of 2/3 ...
- Math - Suppose you toss a coin and will win $1 if it comes up heads. If it comes...
- MATH - Suppose you toss a coin and will win $1 if it comes up heads. If it comes...
- Finite! please help - an unfair coin with pr[tails]= .15 is flipped 6 times. ...
- math - Assume that the coin is flipped 10 times. What is the probability that ...

More Related Questions