Question

Artie has a book of short stories. The number of each type of short story is shown below.
• 6 science-fiction stories
• 4 adventure stories
• 3 historical stories
• 2 sports stories

He selects one short story at random. What is the probability that the story Artie selects is either a science-fiction story or an adventure story?

A.) 1/2
B.) 2/1
C.) 1/3
D.) 2/3

Answer 1

we are given

• 6 science-fiction stories

• 4 adventure stories

• 3 historical stories

• 2 sports stories

so,

total number of stories =6+4+3+2

total number of stories =15

Probability of selecting science stories:

number of science stories =6

total number of stories =15

P(S)=(number of science stories)/(total number of stories)

$p(S)=\frac{6}{15}$

$p(S)=\frac{2}{5}$

Probability of selecting adventure stories:

number of adventure stories =4

total number of stories =15

P(A)=(number of adventure stories)/(total number of stories)

$p(A)=\frac{4}{15}$

$p(A)=\frac{4}{15}$

now, we can find

the probability that the story Artie selects is either a science-fiction story or an adventure story

that is P(AUS)

p(AUS)=p(A)+p(S)-p(A∩S)

we know that

p(A) and p(S) are independent

so,

p(A∩S)=p(A)*p(S)

we can plug it

p(AUS)=p(A)+p(S)-p(A)*p(S)

we get

p(AUS)=$\frac{2}{5}+\frac{4}{15}-  \frac{2}{5}*\frac{4}{15}$

p(AUS)=$\frac{14}{25}$...........Answer