You’re invited to play a game! You pay $10 to then pick one envelope out of a dr

Question

You’re invited to play a game! You pay $10 to then pick one envelope out of a drum full of 100 identical envelopes. Each of the envelopes contains a coupon for a free gift:

Four of the coupons are for a free gift worth $40

Six of the coupons are for a free gift worth $12

Eighty (80) of the coupons are for a free gift worth $8

Ten of the coupons are for a free gift worth $6.

a) .What is the probability that a single randomly-selected envelope contains a coupon for a free gift worth $12 or more?

b) What is the expected value of this game? Is it financially worth playing?

c) Find the standard deviation of x (coupon value)

Explanation / Answer

a) probability that a single randomly-selected envelope contains a coupon for a free gift worth $12 or more = 46/100 = 0.46

b)  Expected value = 0.04*40+0.06*12+0.80*8+0.10*6-10 = -0.68

So , it is not financially worth playing

c) Variance = 40*40*0.04+12*12*0.06+8*8*0.08+6*6*0.1-(9.32*9.32) = 40.5776

Standard deviation = Sqrt(40.5776) = 6.37 (rounded to two decimal places)

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.