Respuesta :
Answer:
The probability that my sister's business will still open at the end of the first year is 0.541.
Step-by-step explanation:
The events are denoted as:
A = A new small business closes before the end of its first year.
B = New business started by a woman.
It is provided that:
P (A) = 0.42
P (B) = 0.37
P (A ∪ B) = 0.62
The probability that my sister's business will still open at the end of the first year is expressed as [tex]P(\bar A|B)=\frac{P(\bar A\cap B)}{P(B)}[/tex].
The value of [tex]P(\bar A\cap B)=P(B)-P(A\cap B)[/tex].
Compute the value of P (A ∩ B) as follows:
[tex]P(A\cap B)=P(A) + P(B) - P(A\cup B)=0.42+0.37-0.62=0.17[/tex]
The value of [tex]P(\bar A\cap B)[/tex] is:
[tex]P(\bar A\cap B)=P(B)-P(A\cap B)=0.37-0.17=0.20[/tex]
Compute the value of [tex]P(\bar A|B)[/tex] as follows:
[tex]P(\bar A|B)=\frac{P(\bar A\cap B)}{P(B)}=\frac{0.20}{0.37}=0.54054\approx0.541[/tex]
Thus, the probability that my sister's business will still open at the end of the first year is 0.541.
