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VashaNatasha [74]
3 years ago
5

A computer program contains one error. In order to find the error, we split the program into 6 blocks and test two of them, sele

cted at random. Let X be the number of errors in these blocks. Compute E(X).
Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
7 0
There are \dbinom62 ways of selecting two of the six blocks at random. The probability that one of them contains an error is

\dfrac{\dbinom11\dbinom51}{\dbinom62}=\dfrac5{15}=\dfrac13

So X has probability mass function

f_X(x)=\begin{cases}\dfrac13&\text{for }x=1\\\\\dfrac23&\text{for }x=0\end{cases}

These are the only two cases since there is only one error known to exist in the code; any two blocks of code chosen at random must either contain the error or not.

The expected value of finding an error is then

\displaystyle\sum_{x=0}^1xf_X(x)=0\times\dfrac23+1\times\dfrac13=\dfrac13
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