Question

Suppose you repeatedly throw 3 fair coins (simultaneously). How many such throws do expect to do until you get a throw where all coins come up heads?

Answer 1

Answer:

Number of trails required equals 8.

Explanation:

The probability that all three coins have heads as their result equals

$P(E)=P(1)\times P(2)\times P(3)\\\\P(E)=1/2\times 1/2\times 1/2\\\\ \therefore P(E)=\frac{1}{8}$

Now using basic theorem of Geometric probability we have

"If probability of success is p in every trial, then expected number of trials until success is 1/p"

Thus the no of trails until success equals $\frac{1}{\frac{1}{8}}=8$