Respuesta :
Answer:
(a) 0.67 (b) 0.69
(c) 0.85 (d) 0.8254
(e) 0.5146 (f) 0.8254, 0.4854
Step-by-step 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) = 0.67, P (B) = 0.69 and P (B | A) = 0.85
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) = 0.67.
(b)
The probability that a new store grosses over $940,000 its second year is:
P (B) = 0.69.
(c)
The probability that a store that showed a profit the first year also showed a profit the second year is:
P (B | A) = 0.85.
(d)
The probability that a store showed profit in both the first and second year is:
[tex]P(A\cap B)=\frac{P(B|A)P(A)}{P(B)} =\frac{0.85\times0.67}{0.69} =0.8254[/tex]
Thus, the value of P (A and B) is 0.8254.
(e)
The probability that a store showed profit in either the first or the second year is:
[tex]P(A\cup B)=P(A) + P(B) - P(A\cap B)=0.67+0.69-0.8254=0.5146[/tex]
Thus, the value of P (A or B) is 0.5146.
(f)
A store will be closed if it does not shows the profit in the first 2 years.
The probability that the Wing foot store will not be closed after 2 years is:
P (Wing foot will show profit for both 2 years) = P (A and B) = 0.8254.
Thus, the probability that the Wing foot store will not be closed after 2 years is 0.8254.
The probability that the Wing foot store will be closed after 2 years is:
P (Wing foot will not show profit for any of the 2 years) = P (neither A nor B)
[tex]=P(A^{c}\cup B^{c})\\=1-P(A\cup B)\\=1-0.5146\\=0.4854[/tex]
Thus, the probability that a new store will be closed after 2 years is 0.4854.
