Question

Two hundred people were surveyed about whether or not they like recreational reading and academic reading. The following two-way table displays data for the sample of people who responded to the survey.
Opinion Liked academic reading Disliked academic reading TOTAL
Liked recreational reading 136136136 404040 176176176
Disliked recreational reading 161616 888 242424
TOTAL 152152152 484848 200200200
In this sample, are the events "liked recreational reading" and "disliked recreational reading" mutually exclusive?

Answer 1

Answer:

Yes, the events "liked recreational reading" and "disliked recreational reading"  are mutually exclusive.

Step-by-step explanation:

Mutually exclusive is another word for disjoint.

Two events A and B are said to be mutually exclusive if:

                 $P(A\bigcap B)=0$

The two-way frequency table could be seen from the attached figure.

If here A denote the event liked recreational rating and B denote the event disliked recreational reading.

Then obviously such events are mutually exclusive.

Since, he has just two choices whether he will love a particular thing or not.

Answer 2

Yes. the two events, e.g. LIKED and DISLIKED cannot both be TRUE at the same time