Difficulty Understanding Something...

Hi everybody,

If a problem were asked, for example:

10 coins are flipped. What is the probability that 10 are heads?

Naturally, I would say, the probability of one coin being heads is .5, so, the probably of 8 coins being heads would be .5 * .5 * .5 * .5 * .5 * .5 * .5 * .5 or .5^8.

That's just what makes sense to me, and equals .0039.

However, the book goes about this question a very strange way. In my chapter on Binomial distribution, it uses combinations and says:

10 C 8 * (.5)^8 * (.5)^2

This method yields .043, which is supposedly the correct answer. These two methods are different and their answers are different. This entire chapter on binomial distribution is very bizare to me and makes no logical sense to me.

If anybody can help me understand why on earth this makes sense, I would appreciate it.

Thanks!

Ethan

10 coin flips-probalbility of 2 tails 8 heads

originally posted by ethan davis. answered by others p= 0.044

in the hope of clarifying the answer for ed here is another approach.

when a coinis flipped there are two outcomes.on the next flip two more outcomes making 2x2=4 outcomes. next 2x2x2=8outcomes. after 10 flips the outcomes total 2E10 or 1024. these are all the possible outcomes.

for exactly 2 tails these can show up on only two of the 10 flips(1-10) but which number flips.so the question is how many two flip numbers can be generated from the ten.this is the number of two nunber combinations from the ten or (10) =45 these are favorable

2

probability_favorable outcomes 45/2E10=0.044

total outcomes