Question

There are 10 chips in a bag. There 2 blue chip(s), 6 red chip(s), and 2 white chip(s). A player gets to draw one chip from the bag. If a blue chip is drawn, the player wins $10. If a red chip is drawn, the player wins $5. If a white chip is drawn, the player wins $1. Someone decides to play the game, hoping to win some money. It costs 5 to play the game.

a) What is the net profit and probability of drawing a blue chip? Net Profit:                 Probability:

b) What is the net profit and probability of drawing a red chip? Net Profit:                   Probability:

c) What is the net profit and probability of drawing a white chip? Net Profit:               Probability:

d) What is the expected value (expected profit) from playing the game?

Answer 1

a) If a blue chip is drawn, the player wins $10 and  It costs $5 to play the game. so Net Profit: 10-5=$5

Probability of drawing a blue chip, There are 2 blue chips out of which player can select one chip in = 2 ways

and in total we have 10 chips out of which player can select one chip in = 10

Hence, Probability of drawing a blue chip= 2/10 =0.2

b) simillary,

If a red chip is drawn, the player wins $5 and  It costs $5 to play the game. so Net Profit: 5-5= $ 0

Probability of drawing a red chip=6/10 =0.6

c)

If a white chip is drawn, the player wins $1 and  It costs $5 to play the game. so Net Profit: 1-5= $ -4

Probability of drawing a red chip=2/10 =0.2

d) expected value (expected profit) from playing the game= profit if that color chip is drown * probability of that color

= 10*0.2+5*0.6+1*0.2

= $ 5.2

I hope you get it.

Cheers.