Respuesta :
Answer:
(a) The probability that a mower manufactured at the Buffalo factory will pass the quality control check is 0.65.
(b) The probability that a mower was manufactured in Dallas given that it passes the quality check is 0.4861.
Step-by-step explanation:
Denote the events as follows:
X = a mower is manufactured at the Portland factory
Y = a mower is manufactured at the Dallas factory
Z= a mower is manufactured at the Buffalo factory
A = a mower passes the quality check.
The information provided is:
[tex]P(X)=0.30\\P(A|X)=0.80\\P(Y)=0.50\\P(A|Y)=0.70\\P(Z)=0.20\\P(A)=0.72[/tex]
(a)
The probability that a mower manufactured at the Buffalo factory will pass the quality control check is:
P (A|Z)
Compute the value of P (A|Z) as follows:
[tex]P(A)=P(A\cap X)+P(A\cap Y) + P (A\cap Z)\\0.72=(0.80\times0.30)+(0.70\times0.50)+(0.20\times P(A|Z))\\0.20\times P(A|Z)=0.72-0.24-0.35\\P(A|Z)=\frac{0.13}{0.20}\\=0.65[/tex]
Thus, the probability that a mower manufactured at the Buffalo factory will pass the quality control check is 0.65.
(b)
Compute the value of P (Y|A) as follows:
[tex]P(Y|A)=\frac{P(A|Y)P(Y)}{P(A)}=\frac{0.70\times0.50}{0.72}=0.4861[/tex]
Thus, the probability that a mower was manufactured in Dallas given that it passes the quality check is 0.4861.
