Question

the following data represent the number of different communication activities used by a random sample of teenagers in a given week. complete parts (a) through (d).
activities 0 1 - 2 3 - 4 5 + total
male 22 81 60 37 200
female 22 51 57 70 200
total 44 132 117 107 400
(a) are the events \male\ and \0 activities\ independent?
yes, because p(male) and p(male|0 activities) are equal.
(b) are the events \female\ and \5 + activities\ independent?
no, because p(female) and p(female|5 + activities) are not equal.
(c) are the events \1 - 2 activities\ and \5 + activities\ mutually exclusive?
<dropdown> because <dropdown> is <dropdown>

Explanation:

Step1: Recall the definition of mutually - exclusive events

Two events A and B are mutually exclusive if \(P(A\cap B)=0\), that is, they cannot occur at the same time.

Step2: Analyze the events "1 - 2 activities" and "5+ activities"

A teenager cannot use 1 - 2 communication activities and 5+ communication activities in the same week. So the number of teenagers who use 1 - 2 activities and 5+ activities simultaneously is 0. Let event A be "1 - 2 activities" and event B be "5+ activities". Then \(P(A\cap B) = 0\).

Answer:

Yes, because the probability of both events occurring simultaneously is 0.