we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
The probability is the size of the event space divided by the size of the sample space
Part 1) What is the probability that the book chosen is a science fiction book?
Let
x--------> the size of the event space
y-------> the size of the sample space
P------> probability
\(P=\frac{x}{y}\)
in this problem we have
\(x=14\ books\\y=30\ books\)
substitute
\(P=\frac{14}{30}\)
Simplify
\(P=\frac{7}{15}\)
therefore
the answer part 1) is the option C
\(\frac{7}{15}\)
Part 2) Marlene is a tennis player who has won \(55\%\) of her tennis matches. What is the probability that she will lose her next tennis match?
we know that
the probability that she won is \(55\%\)
so
the probability that she will lose is \(100\%-55\%=45\%\)
therefore
the answer Part 2) is the option C
\(45\%\)
Part 3) Six tiles lettered B,A,N,A,N and A are lying face down on a table . A tile is selected, the letter is recorded, the tile is replaced, and the process is repeated. What is the theoretical probability of selecting the letter A
Let
x--------> the size of the event space
y-------> the size of the sample space
P------> probability
\(P=\frac{x}{y}\)
in this problem we have
\(x=3\ letters\ A\\y=6\ total\ letters\)
substitute
\(P=\frac{3}{6}\)
Simplify
\(P=\frac{1}{2}\)
therefore
the answer Part 3) is the option D
\(\frac{1}{2}\)
