Question

3. You are a senior consultant at a highly prestigious agency. You did a great job in 2020,

which means you are eligible for a bonus payment.
Your boss gives you three options:
1. You flip a coin 10 times, and for every head you obtain $2,000.
2. You roll three dice and obtain $1,000 for every dot you count.
3. You get paid $9,000.

(a) Which option has the highest expected payout? Justify your answer.

(b) Which options are acceptable to you, if you want to be at least 95% sure to obtain
at least $6.000? Justify your answer.

(c) Which option should you choose to maximise your chances for a $16.000 bonus
payment? Justify your answer.​

Answer 1

(a)The highest expected payout option 1

(b)1 and 3

(c)Option 1

Explanation:

In this you just multiply the amount you are paid by chance if all are favorable to you, so in option 1 you would get $2,000 for each head you get on a flipped coin, so that would be 10*$2,000=$20,000 that's the highest paid, in the dice you get a maximum of 6 dots each, that would make $6,000*3=$18,000.

Rolling the dice can get you 5 scenarios where you don't get $6,000 when all three are lower than $6,000 which would be getting three 1's, two 1's and a 2, ot two 2's and a 1. That's why only option 3 and 1 are available for an almost certainity of getting $6,000

To know this you have to remember last problem, the getting $9,000 will never give you $16,000, and the dice would give you only 3 scenarios where you could end up winning $16,000 whihc would be getting all 6's, two 6's and a 5, or twop 5's and a 6, so your best option would be flipping the coin.