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
(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?
yes, because p(1 - 2 activities and 5 + activities) is zero.
(d) are the events \male\ and \1 - 2 activities\ mutually exclusive?
<select> because <select> is <select>

Explanation:

Step1: Recall the definition of mutually - exclusive events

Two events A and B are mutually exclusive if \(P(A\cap B)=0\).

Step2: Check the number of males with 1 - 2 activities

From the table, the number of males with 1 - 2 activities is 81. So \(P(\text{male and }1 - 2\text{ activities})
eq0\).

Answer:

No, because \(P(\text{male and }1 - 2\text{ activities})\) is non - zero.