Respuesta :
Answer:
(a) The odds for and against E are (8:1) and (1:8) respectively.
(b) The odds for and against E are (7:2) and (2:7) respectively.
(c) The odds for and against E are (59:41) and (41:59) respectively.
(d) The odds for and against E are (71:29) and (29:71) respectively.
Step-by-step explanation:
The formula for the odds for an events E and against and event E are:
[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}[/tex]
(a)
The probability of the event E is:
[tex]P(E)=\frac{8}{9}[/tex]
Compute the odds for and against E as follows:
[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{8/9}{1-(8/9)}=\frac{8/9}{1/9}=\frac{8}{1}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-(8/9)}{8/9}=\frac{1/9}{8/9}=\frac{1}{8}[/tex]
Thus, the odds for and against E are (8:1) and (1:8) respectively.
(b)
The probability of the event E is:
[tex]P(E)=\frac{7}{9}[/tex]
Compute the odds for and against E as follows:
[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{7/9}{1-(7/9)}=\frac{7/9}{2/9}=\frac{7}{2}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-(7/9)}{7/9}=\frac{2/9}{7/9}=\frac{2}{7}[/tex]
Thus, the odds for and against E are (7:2) and (2:7) respectively.
(c)
The probability of the event E is:
[tex]P(E)=0.59[/tex]
Compute the odds for and against E as follows:
[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{0.59}{1-0.59}=\frac{0.59}{0.41}=\frac{59}{41}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-0.59}{0.59}=\frac{0.41}{0.59}=\frac{41}{59}[/tex]
Thus, the odds for and against E are (59:41) and (41:59) respectively.
(d)
The probability of the event E is:
[tex]P(E)=0.71[/tex]
Compute the odds for and against E as follows:
[tex]\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{0.71}{1-0.71}=\frac{0.71}{0.29}=\frac{71}{29}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-0.71}{0.71}=\frac{0.29}{0.71}=\frac{29}{71}[/tex]
Thus, the odds for and against E are (71:29) and (29:71) respectively.
