Year 12s: what will be the first way you research your future options? >>

when to use binomial expansion

a question says a bias diced p(h) 2/3
find P the first tail will occur on the sixth toss
and in the book they did (2/3)^5 x (1/3)= 32/729
but another question
in the first 8 tosses there will be exactly 2 tails
and here they use binomial expansion
why couldn't of i used binomial expansion in the first one ? when i do use the answer is wrong

Reply 1

interlanken-fall

is it because for the second question it will be randomly placed so we don't know so can have multiple places while the first one we know exactly where it will be so no need for binomial expansion

Reply 2

ghostwalker

Original post by interlanken-fall

is it because for the second question it will be randomly placed so we don't know so can have multiple places while the first one we know exactly where it will be so no need for binomial expansion

That is true.

In the second case, there are 2 tails out of 8 tries, and those two tails could be anywhere in the 8.

In the first case, you have 5 heads, and then the tail. If you try it via binomial with n=6, then you'd be working out the probability of 1 tail in 6 tries and the 1 tail could be anywhere in the 6 tries. Your value would be 6 times what it should be.