Question

Find the probability that a randomly selected person

Answer 1

Answer:

The probability that a randomly selected person  from this sample liked recreational reading or disliked recreational reading is 1.

Step-by-step explanation:

The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

Mutually exclusive events are those events which cannot occur together. They are also known as disjoint events.

If events A and B are mutually exclusive then:

$P(A\cap B)=0$

The data provided is:

Opinion                      Like academic     Dislike academic      Total

                                          reading              reading

Liked recreational                   136                      40                      176

reading

Disliked recreational                16                        8                        24

reading

Total                                       152                      48                      200

Denote the events as follows:

X = a person liked recreational reading.

Y = a person disliked recreational reading.

Compute the probability that a randomly selected person  from this sample liked recreational reading or disliked recreational reading as follows:

$P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)$

                $=\frac{176}{200}+\frac{24}{200}-0\\\\=\frac{176+24}{200}\\\\=1$

Thus, the probability that a randomly selected person  from this sample liked recreational reading or disliked recreational reading is 1.