# What is the probability of heads in unfair coin when you flip the coin ten times? [closed]

What is the probability of heads in unfair coin when you flip the coin ten times?

i came across this question and I haven't figured it out

Suppose that you flip an unfair coin ten times, where p(heads)=3/4 and p(tails)= 1/4, Find probability of

1.p(no heads)

5.p(number of heads greater than number of tails)


i hop this help

Thanks

## closed as off-topic by Namaste, Shailesh, Leucippus, KReiser, Key FlexNov 25 '18 at 1:11

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• Please keep in mind that this is not a free homework solution service. – Aditya Dua Nov 25 '18 at 7:18

1. Probability of no heads: $$\bigg(\frac{1}{4}\bigg)^{10}$$
2. Exactly one head: $$\binom{10}{9}\,\bigg(\frac{1}{4}\bigg)\bigg(\frac{3}{4}\bigg)^9$$
3. Exactly seven heads: $$\binom{10}{7}\,\bigg(\frac{1}{4}\bigg)^3\bigg(\frac{3}{4}\bigg)^7$$
4. At least seven heads: $$\binom{10}{7}\,\bigg(\frac{1}{4}\bigg)^3\bigg(\frac{3}{4}\bigg)^7 + \binom{10}{8}\,\bigg(\frac{1}{4}\bigg)^2\bigg(\frac{3}{4}\bigg)^8 + \binom{10}{9}\,\bigg(\frac{1}{4}\bigg)\bigg(\frac{3}{4}\bigg)^9 + \bigg(\frac{3}{4}\bigg)^{10}$$