Financial/Analytical Question2

For each of the following 4 alternatives:

 

i) calculate the expected value (EV) of the coin flip option and briefly explain your logic. Note the amount certain is also an expected value (EV);

 

ii) calculate the minimum number of successes (HEADS) for the coin flip option to equal or exceed the amount certain;

 

iii) use Stat Trek to calculate the probability that the minimum number of successes above will be achieved;

(HINT: Google “Stat Trek Binomial Calculator”)

 

iv) for each of the 3 alternatives, which option would you choose (i.e. the “coin flips” or the “amount certain”)? Briefly explain?

 

 

 

ALTERNATIVE#1

 

 

 

a) $50,000

 

OR

 

b) 10 coin flips each of which has a

 

i) 50% chance of $8,500 (Heads)

 

ii) 50% chance of $2,500 (Tails)

 

EV = $ (for 10 flips)

 

 

MINIMUM NUMBER OF SUCCESSES =

STAT TREK PROBABILITY =

 

YOUR CHOICE of the amount certain or the Coin Flips = (brief explanation)

 

 

 

ALTERNATIVE#2

 

 

. a) $50,000

 

OR

 

b) 100 coin flips each of which has a

 

i) 50% chance of $750 (Heads)

 

ii) 50% chance of $100 (Tails)

 

 

EV = $ (for 100 flips)

 

 

MINIMUM NUMBER OF SUCCESSES =

 

STAT TREK PROBABILITY =

 

YOUR CHOICE of the amount certain or the coin Flips = (brief explanation)

 

 

 

 

 

 

ALTERNATIVE#3

 

 

 

.a) $50,000

 

OR

 

b) a 1000 coin flips with a

 

i) 50% chance of $76 (Heads)

 

ii) 50% chance of $25 (Tails)

 

EV = $ (for 1000 flips)

 

 

MINIMUM NUMBER OF SUCCESSES =

 

STAT TREK PROBABILITY =

 

YOUR CHOICE of the amount certain or the coin Flips = (brief explanation)

 

 

 

 

Binomial Calculator: Online Statistical Table

Use the Binomial Calculator to compute individual and cumulative binomial probabilities. For help in using the calculator, read the Frequently-Asked Questions or review the Sample Problems.

To learn more about the binomial distribution, go to Stat Trek’s tutorial on the binomial distribution.

· Enter a value in each of the first three text boxes (the unshaded boxes). · Click the Calculate button. · The Calculator will compute Binomial and Cumulative Probabilities.   Probability of success on a single trial   Number of trials   Number of successes (x)   Binomial Probability: P(X = 7)   Cumulative Probability: P(X < 7)   Cumulative Probability: P(X < 7)   Cumulative Probability: P(X > 7)   Cumulative Probability: P(X > 7)