I am studying for my midterm test for Stats and I am working on some problems from the textbook. I was hoping to verify my answers which would help me know I am doing the "right" thing. Thank you for your time.
Short version of the question
Nuclear reactor, 10 rods, must have atleast 5 rods working to prevent meltdown. probability of rod being properly inserted incase of an incident 0.80. What is the probability that the system will fail?
My solution
$$\sum^4_{i=0} {10 \choose i}(0.8)^i(0.2)^{10-i}$$
Right.
The probability of success $p=0.8$.
Define a random variable $X = B(10, 0.8)$
$P($reactor fails$) = P(X \le 4)$
Which is prcisely your answer.