Answer:
(a) The odds of event E is 4/3.
(b) The odds of event E is 3/2.
Step-by-step explanation:
Formula for probability of an event:
[tex]Probability=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Formula for odds of an event:
[tex]odds=\frac{\text{Favorable outcomes}}{\text{Unfavorable outcomes}}[/tex]
(a)
It is given that
[tex]P(E)=\frac{4}{7}[/tex]
The probability of unfavorable event
[tex]P(E')=1-P(E)=1-\frac{4}{7}=\frac{3}{7}[/tex]
Odds of event E is
[tex]odds=\frac{P(E)}{P(E')}[/tex]
[tex]odds=\frac{\frac{4}{7}}{\frac{3}{7}}[/tex]
[tex]odds=\frac{4}{3}[/tex]
Therefore the odds of event E is 4/3.
(b)
It is given that
[tex]P(E)=0.6[/tex]
The probability of unfavorable event
[tex]P(E')=1-P(E)=1-0.6=0.4[/tex]
Odds of event E is
[tex]odds=\frac{P(E)}{P(E')}[/tex]
[tex]odds=\frac{0.6}{0.4}[/tex]
[tex]odds=\frac{3}{2}[/tex]
Therefore the odds of event E is 3/2.
