Question

$3000$ fair coins are tossed. Find the probability of getting at least $300$ heads, given first coin is tail.

Answer 1

First coin is tail so from remaining 2999 coin we have to get at least 300 heads

Probability of 300 heads=${{2999}_C}_{300}$*${\frac{1}{2}}^{300}\ast {\frac{1}{2}}^{2999-300}$

=${{2999}_C}_{300}$*${\frac{1}{2}}^{2999}$

similarly probability of 301 heads=${{2999}_C}_{301}$*${\frac{1}{2}}^{2999}$

And so on ..

Probability of getting at least 300 heads=${\frac{1}{2}}^{2999}({{2999}_C}_{300}+{{2999}_C}_{301}+{{2999}_C}_{302}+..+{{2999}_C}_{2999})$