Question

In the old days, there was a probability of \(0.8\) of success in any attempt to make a telephone call. (This often depended on the importance of the person making the call, or the operator's curiosity!)
Calculate the probability of having 7 successes in 10 attempts.

Answer 1

Probability of success \(p=0.8\), so \(q=0.2\).
\(X=\) success in getting through.
Probability of 7 successes in 10 attempts:
Probability \(=P(X=7)\)
\[
\begin{aligned}
&=C_{7}^{10}(0.8)^{7}(0.2)^{10-7} \\
&=0.20133
\end{aligned}
\]
Histogram
We use the following function
\[
C(10, x)(0.8)^{x}(0.2)^{10-x}
\]
to obtain the probability histogram: