Respuesta :
The probability that all specimens of one of the two types of rock are selected for analysis is 0.0325
Step-by-step explanation:
Step 1
Given in the question that there are 10 specimens of basaltic rock and 10 specimens of granite.
The Total specimen sample collected =20
Step 2
The probability of selecting a basaltic rock is= 10 / 20 = 0.5
The probability of selecting a granite is= 10 / 20 = 0.5
So, the probability mass function of the number of basalt specimens selected for analysis is given by
[tex]f(x)=\left \ (10\atop x) \right. (0.5)^{x} (0.5)^{10-x}[/tex]
Step 3
The probability that all specimens of one of the two types of rock are selected for analysis is given by the
sum of the probabilities that 10 basalt specimens and 5 igneous specimen is selected and the probabilities that 5 basalt specimens and 10 igneous specimen is selected.
The probability that 10 basalt specimens and 5 igneous specimen is selected is given by
[tex]\left \ ( ^{10}_ {10} )\right \left \ ( ^{10} _{5}) \right/\left \ ( ^{20}_{15}) \right. =252/15504=0.01625[/tex]
The probability that 5 basalt specimens and 10 igneous specimen is selected is also given by
[tex]\left \ ( ^{10}_ {10} )\right \left \ ( ^{10} _{5}) \right/\left \ ( ^{20}_{15}) \right. =252/15504=0.01625[/tex]
Therefore, the probability that all specimens of one of the two types of rock are selected for analysis is given by
Step 4
Multiplying 2 with the output
2(0.01625) = 0.0325
The probability that all specimens of one of the two types of rock are selected for analysis is 0.0325
