Question

the venn diagram below shows the 11 students in mr. baileys class. the diagram shows the memberships for the dance club and the chess club.

note that \milan\, \mary\, \yolanda\, and \manuel\ are outside the circles since they are not members of either club.

one student from the class is randomly selected.
let \\(a\\) denote the event \the student is in the dance club.\
let \\(b\\) denote the event \the student is in the chess 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{ and } b) = \square\\)

\\(p(a \text{ or } 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)\\).

\\(\bigcirc p(b)\\)
\\(\bigcirc p(a \text{ and } b)\\)
\\(\bigcirc p(a)\\)
\\(\bigcirc p(a \text{ or } b)\\)

Explanation:

Count the students in each region of the Venn diagram

$$
LATEXBLOCK0
$$

Calculate the required probabilities

$$
LATEXBLOCK1
$$

Identify the equivalent probability expression

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

Answer:

Question (a)

• \(P(A) = \frac{3}{11}\)
• \(P(B) = \frac{5}{11}\)
• \(P(A \text{ and } B) = \frac{1}{11}\)
• \(P(A \text{ or } B) = \frac{7}{11}\)
• \(P(A) + P(B) - P(A \text{ and } B) = \frac{7}{11}\)

Question (b)

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