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?
Accepted Solution
A:
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: [tex]\bigg( \dfrac{1}{2} \bigg)^2 \left(\begin{array}{cc}3\\0\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^5 \left(\begin{array}{cc}5\\0\end{array}\right) = \dfrac{1}{256} [/tex]
Probability that both have 1 head: [tex]\bigg( \dfrac{1}{2} \bigg)^2 \left(\begin{array}{cc}3\\1\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^5 \left(\begin{array}{cc}5\\1\end{array}\right) = \dfrac{15}{256} [/tex]
Probability that both have 2 heads: [tex]\bigg( \dfrac{1}{2} \bigg)^2 \left(\begin{array}{cc}3\\2\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^5 \left(\begin{array}{cc}5\\2\end{array}\right) = \dfrac{30}{256} [/tex]
Probability that both have 3 heads: [tex]\bigg( \dfrac{1}{2} \bigg)^2 \left(\begin{array}{cc}3\\3\end{array}\right) \bigg( \dfrac{1}{2} \bigg)^5 \left(\begin{array}{cc}5\\3\end{array}\right) = \dfrac{10}{256} [/tex]
Probability of getting the same number of heads = [tex] \dfrac{1}{256} + \dfrac{15}{256} + \dfrac{30}{256} + \dfrac{10}{256} = \dfrac{56}{256} = \dfrac{7}{32} [/tex]