Respuesta :
Answer:
(a) 0.69 (d) 0.798
(b) 0.77 (e) 0.662
(c) 0.77 (f) 0.338
Explanation:
The events are:
A = A new store grosses over $940,000 its first year.
B = A new store grosses over $940,000 its second year.
Given:
P (A) = 0.69, P (B) = 0.77 and P (B | A) = 0.89
Also, the franchise has an administrative policy of closing a new store if it does not show a profit in either of the first 2 years.
(a)
The probability that a new store grosses over $940,000 its first year is:
P (A) = 0.69.
(b)
The probability that a new store grosses over $940,000 its second year is:
P (B) = 0.77.
(c)
The probability that a store that showed a profit the first year also showed a profit the second year is:
P (B | A) = 0.89
(d)
The probability that a store showed profit in both the first and second year is:
[tex]P (A\ and\ B)=\frac{P(B|A)P(A)}{P(B)}=\frac{0.89\times0.69}{0.77}=0.798[/tex]
Thus, the value of P (A and B) is 0.798.
(e)
The probability that a store showed profit in either the first or the second year is:
[tex]P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)=0.69+0.77-0.798=0.662[/tex]
Thus, the value of P (A or B) is 0.662.
(f)
A store will be closed if it does not shows the profit in the first 2 years.
Compute the value of [tex]P(A^{c}\ or\ B^{c})[/tex] as follows:
[tex]P(A^{c}\ or\ B^{c})=1-P(A\ or\ B)=1-0.662=0.338[/tex]
Thus, the probability that a new store will not be closed after 2 years is 0.338.
