Question

we asked soccer fans from among the citys neighborhoods which youth soccer team will win the championship this year. each fan was allowed to vote for one team. the results of our poll appear in the frequency table. rows represent the neighborhoods where fans were polled. columns represent the teams competing for the youth soccer championship. what is the probability of voting for the bears or voting for the flash? event a: voting for the bears event b: voting for the flash use the frequency table to compute the following. p(a) = probability of voting for the bears: p(b) = probability of voting for the flash: probability of voting for the bears and voting for the flash: p(a and b) = probability of voting for the bears or voting for the flash: p(a or b) =

Explanation:

Step1: Calculate P(A)

P(A) is the probability of voting for the Bears. The number of people who voted for the Bears is 64, and the total number of people polled is 268. So, $P(A)=\frac{64}{268}=\frac{16}{67}$.

Step2: Calculate P(B)

P(B) is the probability of voting for the Flash. The number of people who voted for the Flash is 114, and the total number of people polled is 268. So, $P(B)=\frac{114}{268}=\frac{57}{134}$.

Step3: Calculate P(A and B)

Since a person can't vote for both the Bears and the Flash simultaneously, P(A and B) = 0.

Step4: Calculate P(A or B)

Use the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$. Substitute the values: $P(A\ or\ B)=\frac{16}{67}+\frac{57}{134}- 0=\frac{32 + 57}{134}=\frac{89}{134}$.

Answer:

$P(A)=\frac{16}{67}$
$P(B)=\frac{57}{134}$
$P(A\ and\ B)=0$
$P(A\ or\ B)=\frac{89}{134}$