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
<h3>For the second option ( option a) ; If he chooses to answer the question by going with option a</h3>
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
<h3>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 = </h3>
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
