A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select

Total number of specimen is 20 (10+10). So, the probability that a randomly selected specimen is granite is ${\displaystyle \frac{10}{20}=\frac{1}{2}=0.5}$.
Consider a random variable X which represents the number of granite specimen in the sample.
X will follow binomial distribution with parameters n = 15 and p = 0.5
The p.m.f of X can be defined as:
${\displaystyle P(x=x)=\left(\begin{array}{c}15\\ x\end{array}\right){0.5}^x{(1-0.5)}^{15-x}}$
x=0,1,2,...,15
The probability that number of granite selected for the analysis is greater than 7 can be calculated as:
${\displaystyle P\left(X>7\right)=1-P(x\le 7)}$
${\displaystyle =1-\sum _{x=0}^7\left(\begin{array}{c}15\\ x\end{array}\right){0.5}^x{(1-0.5)}^{15-x}}$
=1-0.5
=0.5
So, the required probability is 0.5