Flip an unfair coin. Find: (a) p, exactly 7 heads (b) p, exactly 7 tails (c) p, atleast 7 heads

Question

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

a) p(exactly 7 heads)
b) p(exactly 7 tails)
c) p(atleast 7 heads)

Hi, I am really new to probability problems. Kindly guide me on how to solve this kind of problem. Thankyou

Answer 1

One coin flip can be interpreted as a Bernoulli trial with success probability $p=\frac{3}{4}$ for heads. Ten coin flips will give us a binomial distribution with parameter $n=10$ and $p=\frac{3}{4}$. The probability for exact $r$ heads is \begin{align} B(n,p,r)=\binom{n}{r}p^r(1-p)^{n-r} \end{align} You have to calculate

• $B(10,0.75,7)$
• $B(10,0.75,3)$
• $B(10,0.75,7)+\ldots +B(10,0.75,10)$