Gravner- probability

Question

Each day, you independently decide, with probability p, to flip a fair coin.
Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first
20 days? (b) What is the probability of getting 10 Heads before 5 Tails?

Comments

(a) 0.176

(b) 0.118 ??

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Naveen Kumar 3

There is an decidability with the probability $p$ for each day. It means that the answer should contain the formula having $p$.

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Oh.. then probability of getting head will be p/2 ,& probability of not getting head will be (1-p/2).

So, (a) $^{20}C_{10}(p/2)^{10}(1-p/2)^{10}$

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@Naveen Kumar 3Why we taking here p/2 

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@Naveen Kumar 3
I also think so.

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@ajaysoni1924  each day we are first flipping a coin with probability p, then getting a head with probability 1/2.

so, P(success)= p*(1/2) =p/2   {both are independent events}

&, P(not success)= (1-p/2)