Question

A fair coin is tossed $8$ times. Find the probability that it shows head
(a) exactly $5$ times
(b) at least once

Answer 1

Given that a fair coin is tossed $8$ times.

The probability of getting head in one toss is $\frac{1}{2}$ and probability of getting tail in one toss is $\frac{1}{2}$.

The probability of getting head exactly $5$ times in $8$ throws is ${{}^{8}C}_5{\left(\frac{1}{2}\right)}^8=\frac{56}{2^8}=\frac{7}{32}$.

The probability of getting head at least once in $8$ throws is $1-(\frac{1}{2}{)}^8=\frac{255}{256}$.