Question

One of the students in this class has created a game and would like for you to play. You have calculated that you will lose the game 45% of the time. At the same time you know that 30% of players will be paid $1 while 20% of players will be paid $2. It is calculated that all other players will receive the $100 prize. What is the expected value for this game? (Enter your solution as a decimal without using the dollar sign).

A bag contains 7 yellow Skittles and 3 red Skittles. A second bag contains 3 two-dollar bills and 2 fifty-dollar bill. You are instructed to reach into the first bag to draw one Skittle. If the Skittle is red, you may draw two bills from the second bag. If the Skittle is yellow, you may draw one bill from the second bag. What is the expected value for this game? (enter your answer as a decimal without using the dollar sign)

Another game involved drawing one card from a standard deck of cards. If you draw a red face card you earn $5. If you draw a black card you are paid $1. If you draw a red ace you will need to draw a second card from the deck (without replacing the first card). If your second card is red you win $80, if it is black you are paid nothing. All other outcomes earn nothing. What is the expected value for this game? (do not round decimals until you get to the final answer ... then enter your answer rounded to the nearest penny - do not use the dollar symbol)

A jury is about to be selected from a group of 14 men and 18 women:

How many ways can a jury of 5 individuals be selected

How many ways can a jury of 5 individuals be selected so that there is exactly 3 women on the jury

How many ways can a jury of 5 be selected so that all 5 individuals are males?

If a jury of 5 is selected, find the probability that there are exactly 4 women on the jury

If a jury of 5 is selected, find the probability that the jury is made up of all women.

Let's say that we need to select a jury of 10 individuals. What is the probability that there are an equal number of males and females on the jury

Answer 1

1) considering that only the winners will get paid

Expected value of game = 0.55×(0.3×1 + 0.2×2 +0.5×100 =0.3+0.4+50) =0.55× 50.7 = 27.885

2) P(red skittle) = 3/10 , P( yellow skittle) =7/10

Expected value = 3/10×(0.3×4 + 0.6×52+ 0.1×100) + 7/10×(0.6×2 + 0.4×50) = 0.3× 42.4 + 0.7×21.2 = 27.56

3) expected value of game = 0.5×1 + 6/52×5 + 2/52×( 25/51×80 + 26/51 ×0)

= 2.5852

4) total number of jury possible of 5 members = ³²C₅ = 201376

Number of Jury with 3 women = ¹⁴C₂ × ¹⁸C₃ = 91 × 816 = 74256

Number of jury with all males = ¹⁴C₅ = 2002

P(exactly 4 women) =( 14 × ¹⁸C₄ )/ ³²C₅

= (14×3060) / 201376 = 0.2127

P( all women ) = ¹⁸C₅ / 201376 = 8568/ 201376 = 0.0425

P( equal male and female ) = ( ¹⁴C₅ ×¹⁸C₅ ) / ³²C₁₀ = 2002×8568 / 64512240 =0.2659