Question

You have made it to the final round of a game show. The announcer asks you the final multiple choicequestion, which has four possible answers, (a), (b), (c), and (d). If you answer the question correctly,you win $1,000,000. After considering the question, you realize you are not sure, but you have yoursuspicions. You think the answer is either choice (a) with probability 60%, or choice (b) with probability40%. You are certain the answer is not choice (c) or (d).
a. Choose not to answer the question. You walk away with $500,000.b. Select an answer (a or b). If you are correct, you win $1,000,000. If you are incorrect, you win only$32,000.c. Phone a friend. In this option, the announcer allows you to call a friend for help.After listening to your friend’s response, you must then answer the question. You know that: * Given thecorrect answer is (a), your friend will say "a" with probability 80%. * Given the correct answer is (b), yourfriend will say "b" with probability 80%.d. Make a decision tree to find your best strategy. In words, what should your strategy be? How muchmoney do you expect to win?

Answer 1

Answer:

The best option is to phone a friend which will yield a total earnings of $ 806,400

Step-by-step explanation:

From the analysis of the question, there is the probability of success and failure.

if he choose not to answer which is the probability of success, his earnings = $500,000.

if he he answers the question correctly, his earnings = $1,000,000 which in the end, is still a success for him

if he answers the question wrongly, his earnings = $32,000

the last option is to phone a friend and he will either choose option a or option b

Probability of choosing option A = 0.6

Probability of choosing option B = 0.4

For the second option ( option a) ; If he chooses to answer the question by going with option a

expected earnings = P(choosing A) x his earnings if correct +  P(choosing B) x his earnings if wrong

= 0.6 x 1,000,000 + 0.4 x 32,000

= $612,000 will be his earning by second option

if he picks the option b = P (choosing B) x his earnings if correct + P(choosing A) x earnings if wrong = 0.4 x 1,000,000 + 0.6 x 32,000

= $419,000

if he chooses the third option of phoning his friend; since his probability of either a or b is like 80% (o.8) if correct and 0.2 (20%) if wrong =

from the P(success) + P( failure) =1

His earnings = Probability of success x earnings if correct + Probability of failure x earnings if incorrect = 0.8 x 1,000,000 + 0.2 x 32,000

= $806,400

from the calculation done, it is apparent that his best option is to go by phoning a friend since that will yield more earnings for him which is greater than his earnings by going for the second options hence the best option is phoning a friend as this will accrue his expected earning to be $ 806,400