one consumer from the survey is selected at random. use reduced fractions for your responses to each of the…

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. For the first question, let $A$ be the event that the consumer is 18 - 24 years old and $B$ be the event that the consumer dislikes Crunchicles. $P(A\cap B)=\frac{21}{300}$ and $P(B)=\frac{63}{300}$. Then $P(A|B)=\frac{\frac{21}{300}}{\frac{63}{300}}=\frac{21}{63}=\frac{1}{3}$.

Step2: Calculate probability of disliking Crunchicles

The probability that a selected consumer dislikes Crunchicles is $P=\frac{\text{Number of consumers who dislike Crunchicles}}{\text{Total number of consumers}}=\frac{63}{300}=\frac{21}{100}$.

Step3: Use the addition - rule of probability

The addition - rule of probability is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event that the consumer is 35 - 55 years old and $B$ be the event that the consumer likes Crunchicles. $P(A)=\frac{93}{300}$, $P(B)=\frac{61}{300}$, and $P(A\cap B)=\frac{19}{300}$. Then $P(A\cup B)=\frac{93 + 61-19}{300}=\frac{135}{300}=\frac{9}{20}$.

Answer:

$\frac{1}{3}$ $\frac{21}{100}$ $\frac{9}{20}$