### 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?

**Answer:**

63 |

256 |

**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:

(

)1 2 ^{4}×^{4}C_{0}× (

)1 2 ^{5}×^{5}C_{0}

=1 512 - The probability of getting 1 heads in both coins will be:

(

)1 2 ^{4}×^{4}C_{1}× (

)1 2 ^{5}×^{5}C_{1}

=20 512 - The probability of getting 2 heads in both coins will be:

(

)1 2 ^{4}×^{4}C_{2}× (

)1 2 ^{5}×^{5}C_{2}

=60 512 - The probability of getting 3 heads in both coins will be:

(

)1 2 ^{4}×^{4}C_{3}× (

)1 2 ^{5}×^{5}C_{3}

=40 512 - The probability of getting 4 heads in both coins will be:

(

)1 2 ^{4}×^{4}C_{3}× (

)1 2 ^{5}×^{5}C_{3}

=5 512 - The probability of getting same number heads in both coins will be a sum of all above individual probabilities:

+1 512

+20 512

+60 512

+40 512 5 512

=126 512

=63 256