Question

use the information to answer the question.
a restaurant is determining if there is a relationship between the weather and customers ordering hot chocolate. let a be the event where it is raining outside. let b be the event where the most popular drink order is hot chocolate.
p(a) = 0.40
p(b) = 0.32
p(a and b) = 0.21
are events a and b dependent or independent? move a word and two symbols to the blanks to complete the sentence.
events a and b are _____ because p(a and b) p(a) __ p(b).
\tdependent\t\t\t\tindependent
=\t≠\t·\t+\t×

Explanation:

Step1: Recall independence formula

For independent events, \( P(A \text{ and } B) = P(A) \times P(B) \). Let's calculate \( P(A) \times P(B) \).
\( P(A) \times P(B) = 0.40 \times 0.32 = 0.128 \)

Step2: Compare with \( P(A \text{ and } B) \)

We know \( P(A \text{ and } B) = 0.21 \). Since \( 0.21
eq 0.128 \), the events are dependent because \( P(A \text{ and } B)
eq P(A) \times P(B) \).

Answer:

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