Question

4.2 theoretical probability. complement. probability: an event and its complement determine the following probabilites. write your answer in the form given in the information in the problem (percent, decimal, or fraction). the probability that a person will get the flu in a given year is 14%. what is the probability a person will not get the flu? % the probability winning a prize at a carnival is 0.11. what is the probability of not winning a prize? the probability of choosing a blue marble out of a jar of marbles is $\frac{13}{34}$. what is the probability of not choosing a blue marble? question help: video written example message instructor submit question

Explanation:

Step1: Recall probability - complement rule

The probability of an event $A$ and its complement $\overline{A}$ satisfy $P(A)+P(\overline{A}) = 1$.

Step2: Calculate non - flu probability

Given $P(\text{flu})=0.14$, then $P(\text{not flu})=1 - 0.14=0.86 = 86\%$.

Step3: Calculate non - winning probability

Given $P(\text{win}) = 0.11$, then $P(\text{not win})=1 - 0.11 = 0.89$.

Step4: Calculate non - blue marble probability

Given $P(\text{blue})=\frac{13}{34}$, then $P(\text{not blue})=1-\frac{13}{34}=\frac{34 - 13}{34}=\frac{21}{34}$.

Answer:

1. $86$
2. $0.89$
3. $\frac{21}{34}$