Question

the venn diagram below shows the 8 students in mr. murphys class.
the diagram shows the memberships for the tennis club and the soccer club.

note that \trey\ is outside the circles since he is not a member of either club.

one student from the class is randomly selected.
let (a) denote the event \the student is in the tennis club.\
let (b) denote the event \the student is in the soccer club.\

(a) find the probabilities of the events below.
write each answer as a single fraction.
(p(a) = \square)
(p(b) = \square)
(p(a \text{ or } b) = \square)
(p(a \text{ and } b) = \square)
(p(a) + p(b) - p(a \text{ and } b) = \square)

(b) select the probability that is equal to (p(a) + p(b) - p(a \text{ and } b)).
\\(p(a)\\)
\\(p(a \text{ or } b)\\)
\\(p(b)\\)
\\(p(a \text{ and } b)\\)

Explanation:

Count the outcomes in each region of the Venn diagram

$$
LATEXBLOCK0
$$

Calculate the probabilities for part (a)

$$
LATEXBLOCK1
$$

Identify the equivalent probability for part (b)

$$ P(A) + P(B) - P(A \text{ and } B) = P(A \text{ or } B) = \frac{7}{8} $$

Answer:

Question 1

(a) Find the probabilities of the events below. Write each answer as a single fraction.

• \(P(A) =\) <blank>\(\frac{3}{8}\)</blank>
• \(P(B) =\) <blank>\(\frac{3}{4}\)</blank>
• \(P(A \text{ or } B) =\) <blank>\(\frac{7}{8}\)</blank>
• \(P(A \text{ and } B) =\) <blank>\(\frac{1}{4}\)</blank>
• \(P(A) + P(B) - P(A \text{ and } B) =\) <blank>\(\frac{7}{8}\)</blank>

Question 2

(b) Select the probability that is equal to \(P(A) + P(B) - P(A \text{ and } B)\).

• \(P(A)\)
• \(P(A \text{ or } B)\) (Correct answer)
• \(P(B)\)
• \(P(A \text{ and } B)\)