Question

we polled theme - park enthusiasts from around the country about their favorite amusement parks and attractions. the results are broken down in the following frequency table by park name and attraction type. assume that each voter got to choose only one favorite park and one favorite type of attraction. rows represent the different amusement parks from around the country. columns represent the different types of theme - park attractions. what is the probability of choosing eight pennants as a favorite park or choosing a water slide as a favorite ride? event a: choosing eight pennants as a favorite park event b: choosing a water slide as a favorite ride use the frequency table to compute the following. p(a)= probability of choosing eight pennants as a favorite park: p(b)= probability of choosing a water slide as a favorite ride: probability of choosing eight pennants as a favorite park and choosing a water slide as a favorite ride: p(a and b)= probability of choosing eight pennants as a favorite park or choosing a water slide as a favorite ride: p(a or b)=

Explanation:

Step1: Calculate P(A)

The total number of people polled is 264. The number of people who chose Eight Pennants as a favorite park is 94. So, $P(A)=\frac{94}{264}=\frac{47}{132}$.

Step2: Calculate P(B)

The number of people who chose a water - slide as a favorite ride is 76. So, $P(B)=\frac{76}{264}=\frac{19}{66}$.

Step3: Calculate P(A and B)

The number of people who chose Eight Pennants as a favorite park and a water - slide as a favorite ride is 6. So, $P(A\ and\ B)=\frac{6}{264}=\frac{1}{44}$.

Step4: Calculate P(A or B)

Use the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$. Substitute the values: $\frac{47}{132}+\frac{19}{66}-\frac{1}{44}=\frac{47 + 38- 3}{132}=\frac{82}{132}=\frac{41}{66}$.

Answer:

$P(A)=\frac{47}{132}$
$P(B)=\frac{19}{66}$
$P(A\ and\ B)=\frac{1}{44}$
$P(A\ or\ B)=\frac{41}{66}$