**Problem 11A**

Suppose and are independent binomial variables with the following probability functions:

Calculate the following sum:

**Problem 11B**

Suppose and are independent binomial variables with the following probability functions:

Calculate the following sum:

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**Answers**

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**Hint**

Performing the calculation as the problem is stated is a trap. Falling for this trap could be costly. Note that the sum of the two random variables is also a binomial distribution and that the required calculation is merely a probability calculation of the sum. To see this, write out the probability function of the independent sum using the convolution method.

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*Related*

I would like to see the solution for 11-a.

For 11-a I’m getting [(5C0)(5C4)+(5C1)(5C3)+(5C2)(5C2)+(5C3)(5C1)+(5C4)(5C0)]*(0.6^4)(0.4^16)… which differs from your answer…

And I can’t see any other way around calculating it this way.