Questions: A sample of 250 internet users was selected. Find the complements of the following events. Part 1 of 4 (a) More than 150 of them use Google as their primary search engine. The complement is: Fewer than 151 of them use Google as their primary search engine. Part 2 of 4 (b) At least 150 of them use Google as their primary search engine. The complement is: Fewer than 150 of them use Google as their primary search engine.

Solution Steps

To find the complement of an event, we need to consider all outcomes that are not part of the original event. For a given event, the complement includes all possibilities that do not satisfy the condition of the event.

(a) The event is "More than 150 of them use Google as their primary search engine." The complement of this event is "150 or fewer of them use Google as their primary search engine."

(b) The event is "At least 150 of them use Google as their primary search engine." The complement of this event is "Fewer than 150 of them use Google as their primary search engine."

We are given two events related to internet users who use Google as their primary search engine.

1. Event (a): More than 150 users use Google.
2. Event (b): At least 150 users use Google.

To find the complements of these events, we need to express what it means for the events not to occur.

1. For event (a), the complement is: \[ \text{Complement of (a)}: \text{Fewer than or equal to 150 users use Google} \quad \Rightarrow \quad n \leq 150 \]

2. For event (b), the complement is: \[ \text{Complement of (b)}: \text{Fewer than 150 users use Google} \quad \Rightarrow \quad n < 150 \]

Final Answer