### Coin A is flipped 4 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?

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**Answer: **

**Step by Step Explanation: **- The situation of having the same number of heads obtained will occur when 0, 1, 2, 3, and 4 heads appear in both the coins.

So, let's find the individual probability for each scenario and then we will add the probabilities to find the probability of combined scenarios. - The probability of getting 0 heads in both coins will be:

( )^{4} × ^{4}C_{0} × ( )^{5} × ^{5}C_{0}

= - The probability of getting 1 heads in both coins will be:

( )^{4} × ^{4}C_{1} × ( )^{5} × ^{5}C_{1}

= - The probability of getting 2 heads in both coins will be:

( )^{4} × ^{4}C_{2} × ( )^{5} × ^{5}C_{2}

= - The probability of getting 3 heads in both coins will be:

( )^{4} × ^{4}C_{3} × ( )^{5} × ^{5}C_{3}

= - The probability of getting 4 heads in both coins will be:

( )^{4} × ^{4}C_{3} × ( )^{5} × ^{5}C_{3}

= - The probability of getting same number heads in both coins will be a sum of all above individual probabilities: + + + +

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