Question

use the information to answer the question.
aimee and bree each play volleyball on different teams in the same league. let a be the event that aimees team wins a game. let b be the event that brees team wins a game.
p(a) = 0.55
p(b) = 0.60
p(a and b) = 0.29
are events a and b dependent or independent? move the options to the lines to complete the sentence.
the events a and b are ____ because p(a and b) p(a) __ p(b).
options: dependent, independent, =, ≠, +, ×

Explanation:

Step1: Recall independence formula

For independent events, \( P(A \text{ and } B) = P(A) \times P(B) \).

Step2: Calculate \( P(A) \times P(B) \)

\( P(A) = 0.55 \), \( P(B) = 0.60 \), so \( P(A) \times P(B) = 0.55 \times 0.60 = 0.33 \).

Step3: Compare with \( P(A \text{ and } B) \)

Given \( P(A \text{ and } B) = 0.29 \). Since \( 0.29
eq 0.33 \), \( P(A \text{ and } B)
eq P(A) \times P(B) \).

Step4: Determine dependence

If \( P(A \text{ and } B)
eq P(A) \times P(B) \), events are dependent.

Answer:

The events \( A \) and \( B \) are \(\boldsymbol{\text{dependent}}\) because \( P(A \text{ and } B) \boldsymbol{
eq} P(A) \boldsymbol{\times} P(B) \).