Assume that a video game library contains three types of games: role playing gam

Question

Assume that a video game library contains three types of games: role playing games, sports themed games, and puzzle games. Each game falls into one, and only one, of these categories. The library contains 360 puzzle games, 180 role playing games, and 60 sports games. Each game has a rating of either kids or adults (but not both). One fourth of the games are adult games, and the rest are kid’s games. Furthermore assume there are an equal number of adult role playing games, adult sports games, and adult puzzle games in the library. A game is picked randomly from the library.

a) Find the probability of picking a sports game.

b) Find the probability of picking an adult game or a game that is not a sports game.

c) Find the probability of picking an adult game given that we know it is a sports game.

Explanation / Answer

R - role playing (180)
S - sports (60)
P - puzzle (360)

Total 600 games.
1/4th of 600 are adult games hence 150 adult games.

As there are equal number of R, S and P for adults hence each has 50 games

a) There are total 60 sports games
Hence probability, P(S) = 60/600 = 1/10 = 0.1

b)
P(Adult game) = P(A) = 150/600 = 1/4 = 0.25
P(S') = 1 - P(S) = 0.9

P(A and S') = 100/600 = 1/6 (probility of non sports adult game)

Required probability, P(A or S') = P(A) + P(S') - P(A and S')
= 1/4 + 9/10 - 1/6
= 0.9833

c)
P(A and S) = 50/600 = 1/12 = 0.0833
Required probability
P(A|S) = P(A and S)/P(S)
= 0.0833/0.1 = 0.833

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