Answer:
17: 45%
18: dependent events
19: probability that a student selected at random
is a freshman who plays an instrument is 50%
Step-by-step explanation:
Question 18:
P(Junior) = junior / total
total is junior + sophomore
P(Junior) = 24 + 22 / (24 + 22) + (16 + 18)
P(Junior) = 46 / 80 → 23 / 40 simplified by dividing by 2
P(Junior) = 0.58
P(Junior | robotics) = P(junior and robotics) / P(robotics)
P(Junior | robotics) = (24 / 80) / (40 / 80)
P(Junior | robotics) = (3) / (5)
P(Junior | robotics) = 0.6 (this is what you found in question 14)
P(Junior | robotics) ≠ P(Junior)
0.6 ≠ 0.58
They are dependent events
Question 19:
P(instrument) = 40% (given)
P(freshman and instrument) = 20% (given)
P(freshman | no instrument) = 30% (given)
P(freshman | instrument) = P(freshman and instrument) / P(instrument)
P(freshman | instrument) = 0.2 / 0.4
P(freshman | instrument) = 0.5 x 100
P(freshman | instrument) = 50%
I would also like to clairfy Question 17:
P(Sophomore | Game Design) =
P(Sophomore) = sophomore / total
total is junior + sophomore = 80
P(Sophomore) = 16 + 18 / 80
P(Sophomore) = 34 / 80
P(Sophomore | Game Design) =
P(Sophomore and Game Design) / P(Game Design)
P(Sophomore and Game Design) = 18 / 80
P(Game Design) = 18 + 22 / 80
P(Game Design) = 40 / 80
P(Sophomore | Game Design) = (18 / 80) / (40 / 80)
P(Sophomore | Game Design) = 0.45 x 100
P(Sophomore | Game Design) = 45%
you were correct, good job :)
Let me know if you have any questions !!
