Get the information you need quickly and easily with IDNLearn.com. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
If we roll a dice three times and we can stop in the first time only when it come 6. The expected payoff is 4.557.
According to the question:
The number of times you can get 06 are:
(i). If the third toss rolls a 6: 6
In this case her first two digits can be any of the five numbers. No. The number of cases is 5 × 5 = 25.
(ii). If you get a 6 on the second throw. The number of cases is -5 (no third throw in this case)
(iii). If the first roll rolls a 6. The number of cases is -1.
2. Number of times you can get 5 Are-
(i). If there is only one 5 in 3 rolls . The number of cases will simply be
3 × 4 × 4
(Because there are 5 possibilities in 3 places and 4 in the remaining places.)
(ii). If there are two 5s, the number of cases is 3×4. (Because there are 3 places where 5 cannot exist, and the places are filled with 4 possibilities.)
(iii). If there are three 5s, the number of possibilities is -1.
Similarly, for 4,3,2,1, the number of possibilities is (3*3*3 + 3*3 + 1), (3*2*2 + 3*2 + 1), (3 × 1×1 + 3×1 + 1), 1 each.
So the number of possibilities for 1,2,3,4,5,6 are 1,7,19,37,61,31 respectively .
You can now get the expected profit by taking the weighted average of the numbers with the possible outcome odds.
So the result is (6*31 + 5*61 + 4*37 + 3*19 + 2*7 + 1)/(31+61+37+19+7+1)
which is 711/ 156 = 4.557
Therefore, the expected payout is 4.557.
Learn more about Expected payout:
https://brainly.com/question/24321198
#SPJ4
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.