 # A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select Lennie Carroll 2020-12-30 Answered
A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the speciems for analysis
1) What the pmf of the number of granite specimens selected for analysis?
2) What is the probability that the number of granite specimens selected for analysis is greater than 7?
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Total number of specimen is 20 (10+10). So, the probability that a randomly selected specimen is granite is $\frac{10}{20}=\frac{1}{2}=0.5$.
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:
$P\left(x=x\right)=\left(\begin{array}{c}15\\ x\end{array}\right){0.5}^{x}{\left(1-0.5\right)}^{15-x}$
x=0,1,2,...,15
The probability that number of granite selected for the analysis is greater than 7 can be calculated as:
$P\left(X>7\right)=1-P\left(x\le 7\right)$
$=1-\sum _{x=0}^{7}\left(\begin{array}{c}15\\ x\end{array}\right){0.5}^{x}{\left(1-0.5\right)}^{15-x}$
=1-0.5
=0.5
So, the required probability is 0.5