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)
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)
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)=
p(AUS)=...........Answer