Respuesta :
Answer:
a. [tex]\binom{4}{1}\frac{2}{15} ^1(1-\frac{2}{15} )^{3}[/tex]+ [tex]\binom{4}{2}\frac{2}{15} ^2(1-\frac{2}{15} )^{2}[/tex]+ [tex]\binom{4}{3}\frac{2}{15} ^3(1-\frac{2}{15} )^{1}[/tex]+ [tex]\binom{4}{4}\frac{2}{15} ^4(1-\frac{2}{15} )^{0}[/tex]
b. [tex]\binom{4}{1}\frac{8}{15} ^1(1-\frac{8}{15} )^{3}[/tex]+ [tex]\binom{4}{2}\frac{8}{15} ^2(1-\frac{8}{15} )^{2}[/tex]
c. [tex]\binom{4}{3}\frac{1}{3} ^3(1-\frac{1}{3} )^{1}[/tex]
d. [tex](\binom{4}{2}\frac{1}{3} ^2(1-\frac{1}{3} )^{2})[/tex] × [tex](\binom{4}{2}\frac{8}{15} ^2(1-\frac{8}{15} )^{2})[/tex]
e. [tex](1-\binom{4}{0}\frac{1}{3} ^0(1-\frac{1}{3} )^{4})[/tex]× [tex]\binom{4}{3}\frac{2}{15} ^3(1-\frac{2}{15} )^{1}[/tex]
Step-by-step explanation:
Number of cars in lot = 30
Number of cars in great shape = 10
Number of cars in good shape = 16
Number of cars in poor shape = 4
The probability that a car selected is in great shape = 10/30
The probability that a car selected is in good shape = 16/30
The probability that a car selected is in poor shape = 4/30
Therefore, we have
When 4 cars are selected
P(Car is in poor shape) = [tex]\binom{n}{r}p^r(1-p)^{n-r}[/tex]
Where:
p = Probability of success = 2/15
n = Total number of count = 30
r = Number selected = 4
P = [tex]\binom{4}{1}\frac{2}{15} ^1(1-\frac{2}{15} )^{3}[/tex]+ [tex]\binom{4}{2}\frac{2}{15} ^2(1-\frac{2}{15} )^{2}[/tex]+ [tex]\binom{4}{3}\frac{2}{15} ^3(1-\frac{2}{15} )^{1}[/tex]+ [tex]\binom{4}{4}\frac{2}{15} ^4(1-\frac{2}{15} )^{0}[/tex]
b. Here we have
P(At least two cars are in good shape) = [tex]\binom{4}{1}\frac{8}{15} ^1(1-\frac{8}{15} )^{3}[/tex]+ [tex]\binom{4}{2}\frac{8}{15} ^2(1-\frac{8}{15} )^{2}[/tex]
c. P(Exactly 3 cars are in great shape) = [tex]\binom{4}{3}\frac{1}{3} ^3(1-\frac{1}{3} )^{1}[/tex]
d. P(2 Great and 2 Good) = [tex](\binom{4}{2}\frac{1}{3} ^2(1-\frac{1}{3} )^{2})[/tex] × [tex](\binom{4}{2}\frac{8}{15} ^2(1-\frac{8}{15} )^{2})[/tex]
e. P(1 Great and 3 poor) = [tex](1-\binom{4}{0}\frac{1}{3} ^0(1-\frac{1}{3} )^{4})[/tex]× [tex]\binom{4}{3}\frac{2}{15} ^3(1-\frac{2}{15} )^{1}[/tex]
