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.
[tex]P(E)=\frac{n(E)}{N}[/tex]
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:
[tex]P(A\cap B)=0[/tex]
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:
[tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)[/tex]
[tex]=\frac{176}{200}+\frac{24}{200}-0\\\\=\frac{176+24}{200}\\\\=1[/tex]
Thus, the probability that a randomly selected person from this sample liked recreational reading or disliked recreational reading is 1.
