Respuesta :
Answer:
(a) [tex]P(Y'|M)\approx 0.3297[/tex]
(b) [tex]P(Y|M')\approx 0.8323[/tex]
(c) [tex]P(Y'|M')\approx 0.1323[/tex]
Step-by-step explanation:
Given table is
Yes No Don't Know Total
Men 162 92 25 279
Women 258 41 11 310
Total 420 133 36 589
According the the conditional probability, if A and B are two event then
[tex]P(A|B)=P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}[/tex]
We need to find the following probabilities.
Let Y is the event "saying yes," and M is the event "being a man."
(a)
[tex]P(Y'|M)=\frac{P(Y'\cap M)}{P(M)}[/tex]
[tex]P(Y'|M)=\frac{\frac{92}{589}}{\frac{279}{589}}[/tex]
[tex]P(Y'|M)=\frac{92}{279}[/tex]
[tex]P(Y'|M)=0.329749103943[/tex]
[tex]P(Y'|M)\approx 0.3297[/tex]
(b)
[tex]P(Y|M')=\frac{P(Y\cap M')}{P(M')}[/tex]
[tex]P(Y|M')=\frac{\frac{258}{589}}{\frac{310}{589}}[/tex]
[tex]P(Y|M')=\frac{258}{310}[/tex]
[tex]P(Y|M')=0.832258064516[/tex]
[tex]P(Y|M')\approx 0.8323[/tex]
(c)
[tex]P(Y'|M')=\frac{P(Y'\cap M')}{P(M')}[/tex]
[tex]P(Y'|M')=\frac{\frac{41}{589}}{\frac{310}{589}}[/tex]
[tex]P(Y'|M')=\frac{41}{310}[/tex]
[tex]P(Y'|M')=0.132258064516[/tex]
[tex]P(Y'|M')\approx 0.1323[/tex]
