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I need help with 18 and 19

I need help with 18 and 19-example-1
User Alexchernyy
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1 Answer

20 votes
20 votes

Answer:

17: 45%

18: dependent events

19: probability that a student selected at random

is a freshman who plays an instrument is 50%

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 !!

User Thd
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