Respuesta :
It is given that there are 6 books in total, with 2 mysteries, 3 science fiction books, and 1 biography.
Recall that the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.
(a) It is required to find the probability of selecting one mystery and then one science fiction, with replacement.
The probability of selecting one mystery is:
[tex]P(M)=\frac{1}{6}[/tex]The probability of selecting one science fiction next with replacement is:
[tex]P(S)=\frac{1}{6}[/tex]The probability of independent events is the product of their respective probabilities.
Hence, the probability of selecting one mystery and then one science fiction, with replacement is:
[tex]P(M)\cdot P(S)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}[/tex]The answer is 1/36.(b) It is required to find the probability of selecting one mystery and then one science fiction, without replacement.
Since there is no replacement, the probability of selecting one science fiction next without replacement is:
[tex]P(S)=\frac{1}{6-1}=\frac{1}{5}[/tex]Hence, the probability of selecting one mystery and then one science fiction, without replacement is:
[tex]P(M)\cdot P(S)=\frac{1}{6}\cdot\frac{1}{5}=\frac{1}{30}[/tex]The answer is 1/30.