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? because are

Explanation:

Step1: Recall the independence formula

Two events \(A\) and \(B\) are independent if \(P(A\cap B)=P(A)\times P(B)\).

Step2: Calculate probabilities for part (b)

Let \(A\) be the event "female" and \(B\) be the event "5 + activities".

• \(P(A)=\frac{200}{400}=\frac{1}{2}\)
• \(P(B)=\frac{107}{400}\)
• \(P(A\cap B)=\frac{70}{400}\)
• \(P(A)\times P(B)=\frac{1}{2}\times\frac{107}{400}=\frac{107}{800}

eq\frac{70}{400}\)

Answer:

No, because \(P(\text{female})\times P(\text{5 + activities})\) and \(P(\text{female and 5 + activities})\) are not equal.