Question 624479: Consider a couple having four children. We will consider this to be a binomial experiment with the number of trials n equal to 4. Let us assume that success will mean a girl is born, and failure will mean a boy is born (don’t take it personally, guys). The probability of success in any trial, then, is ½, or 0.5.
Write down the formula that gives the probability of Xsuccesses in the 4 trials in this binomial experiment. Simplify as much as possible.
Use your formula to fill in a probability distribution table for X. It should look familiar!
X p(X)
Compute E(X), doing as little work as is needed. Again, your answer should look familiar.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! The probability distribution is given by
x---P(x)
0---1/16
1---4/16
2---6/16
3---4/16
4---1/16
Where 1,4,6,4,1 is the fourth row of Pascal's triangle (which comes from a *binomial* expansion).
The expected value, E(x), is simply (1/2)(4) = 2.
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