In the old days, there was a probability of \displaystyle{0.8}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 \displaystyle{7}7 successes in \displaystyle{10}10 attempts.

In the old days, there was a probability of $\displaystyle{0.8}$ 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 $\displaystyle{7}$ successes in $\displaystyle{10}$ attempts.

 

Answer

Probability of success 

$\displaystyle{p}={0.8}$, so $\displaystyle{q}={0.2}$.

$\displaystyle{X}=$ success in getting through.

Probability of $\displaystyle{7}$ successes in $\displaystyle{10}$ attempts:

$\displaystyle\text{Probability}={P}{\left({X}={7}\right)}$

$\displaystyle={{C}_{{7}}^{{10}}}{\left({0.8}\right)}^{7}{\left({0.2}\right)}^{{{10}-{7}}}$

$\displaystyle={0.20133}$

Histogram

We use the following function

$\displaystyle{C}{\left({10},{x}\right)}{\left({0.8}\right)}^{x}{\left({0.2}\right)}^{{{10}-{x}}}$

to obtain the probability histogram:

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