Question

the probability that event a will occur is p(a) = 0.8. what is the probability (in decimal form) that event a will not occur? p(\overline{a}) = what are the odds for event a? to what are the odds against event a? to simplify your answers.

Explanation:

Step1: Find probability of non - occurrence

The probability of an event $A$ not occurring, $P(\overline{A})$, is given by $P(\overline{A})=1 - P(A)$. Given $P(A)=0.8$, then $P(\overline{A})=1 - 0.8=0.2$.

Step2: Calculate odds for event $A$

The odds for an event $A$ is the ratio of the probability that the event will occur to the probability that it will not occur. Odds for $A=\frac{P(A)}{P(\overline{A})}=\frac{0.8}{0.2}=\frac{4}{1}$, so it is 4 to 1.

Step3: Calculate odds against event $A$

The odds against an event $A$ is the ratio of the probability that the event will not occur to the probability that it will occur. Odds against $A=\frac{P(\overline{A})}{P(A)}=\frac{0.2}{0.8}=\frac{1}{4}$, so it is 1 to 4.

Answer:

$P(\overline{A}) = 0.2$
Odds for event $A$: 4 to 1
Odds against event $A$: 1 to 4