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Let X and Y be independent random variables with distributions B(5, 1/2) and B(7, 1/2), respectively. What is the value of P(X + Y = 3)?
- 35/47
- 55/1024
- 220/512
- 11/204
Correct answer: 55/1024
Solution
Sum of independent binomials with the same p: X+Y~B(12,1/2). So P(X+Y=3)=C(12,3)/2^12=220/4096=55/1024.
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