Respuesta :
Answer:
Step-by-step explanation:
Given that a pie chart shows data as
Excellent 7%
Good 44%
Fair 35%
Poor 13%
Other 1%
If 4 people are chosen at random we find that each person is independent of other and there are two outcomes either excellent or not excellent.
p = Prob for success = p = 7%=0.07
q = Prob for non success = 1-0.07 = 0.93
If x is a random variable representing the excellent persons then X is binomial with n =4, p = 0.07
Required probability = P(X=4)
=[tex]p^4\\=(0.07)^4\\=0.00002401[/tex]
Answer:
0.000022304
Step-by-step explanation:
Total number of people = 1100
Number of people chosen = 4
Excellent percentage is 7% or 0.07
So, number of people rated excellent = [tex]0.07\times1100= 77[/tex]
Others who did not choose excellent = [tex]1100-77=1023[/tex]
So, p(randomly choose 4 excellent)= [tex]\frac{(77C4)(1023C0)}{1100C4}[/tex]
= [tex]\frac{77C4}{1100C4}[/tex]
=[tex]1353275/60671970975[/tex] = [tex]2.2304e^{-5}[/tex]
= 0.000022304
Or second and easy method is simply multiplying:
[tex]\frac{77}{1100} \times\frac{76}{1099} \times\frac{75}{1098} \times\frac{74}{1097}[/tex]
= [tex]32478600/1456127303400[/tex] = 0.000022304
