Question

Coin A is flipped 3 times and coin B is flipped 5 times. What is the probability that the number of heads obtained from flipping the two coins is the same?

Answer 1

There are 4 ways that we will ended up with the same number of heads:
1) When both have 0 head.
2) When both have 1 head.
3) When both have 2 heads.
4) when both have 3 heads.

Probability that both have 0 head:

`\bigg( (1)/(2) \bigg)^2 \left(\begin{array}{cc}3\\0\end{array}\right) \bigg( (1)/(2) \bigg)^5 \left(\begin{array}{cc}5\\0\end{array}\right) = (1)/(256)`

Probability that both have 1 head:

`\bigg( (1)/(2) \bigg)^2 \left(\begin{array}{cc}3\\1\end{array}\right) \bigg( (1)/(2) \bigg)^5 \left(\begin{array}{cc}5\\1\end{array}\right) = (15)/(256)`

Probability that both have 2 heads:

`\bigg( (1)/(2) \bigg)^2 \left(\begin{array}{cc}3\\2\end{array}\right) \bigg( (1)/(2) \bigg)^5 \left(\begin{array}{cc}5\\2\end{array}\right) = (30)/(256)`

Probability that both have 3 heads:

`\bigg( (1)/(2) \bigg)^2 \left(\begin{array}{cc}3\\3\end{array}\right) \bigg( (1)/(2) \bigg)^5 \left(\begin{array}{cc}5\\3\end{array}\right) = (10)/(256)`

Probability of getting the same number of heads =

`(1)/(256) + (15)/(256) + (30)/(256) + (10)/(256) = (56)/(256) = (7)/(32)`