Jim decides to go to the floating casino in Goa. He pays Rs 5000 and gets an entry to the casino along with Rs 25000 worth non cashable play coupons. First he plays game “A” in which he is supposed to bet Rs 5000 worth non cashable play coupons and tosses an unbiased coin 5 times and if at least 4 heads appear, he will get back his Rs 5000 worth non cashable play coupons along with same amount worth cashable play coupons. He continues to play game “A” until all his non cashable play coupons are exhausted. Depending upon the cashable play coupons won in game “A” he will play game “B” for atmost three times, in this game he has to bet a number from 1 to 4 and rotate a wheel of fortune having total six 6’s, five 5’s, four 4’s, three 3’s, two 2’s and one 1 on the wheel. Jim decides to bet Rs 5000 worth cashable coupons every time on number 4 and if he wins he will get Rs 10000 worth cashable play coupons along with the betted amount. Using random numbers 0.12, 0.86, 0.98, 0.65, 0.21, 0.91, 0.82, 0.01, 0.79, 0.31, 0.76 and 0.42 exactly once in the given order, simulate his total profit.
What should be the correct order of simulation? From this I want to ask that how we are going to use these random numbers?
Using these random numbers in a given specific order my professor said that there will be one answer only...
The problem has many solutions depending on how you use the random numbers. As Arthur commented, a simple way is to define each coin flip with one random number, taking the flip as heads if the number is over $0.5$ and tails if it is less. You could then follow his progress through game A, keep track of the number of heads in each group of five flips, and at the end of each group account for how many coupons he has. That would use up many more random numbers than you are allotted. Another way is to use each random number for a whole group of five flips in game A. You know the chance of five heads is $1/32$, so if the random is greater than $31/32$ he got five heads. The chance of exactly four heads is ???, so if the random is in the range ??? to ??? he got four heads. Again, after each group of five flips, using one random number, you can account for his bankroll and keep going. You can even do it all with one random number, though you should have more precision than two digits. You can take the first $0.12$ to say he got the $12$th percentile result for the whole chain. Now model many plays, using the technique at the start of one random per flip or whatever. Rank the results and report the $12$th percentile as the result.
I think the question is asking you to describe some process like the above. There is no one right answer, but you should justify that your process uses no more random numbers than you are given, so the option of one number per flip is not acceptable. It is not clear to me whether you need to guarantee that you need no more than twelve, or just that with the use you make of the randoms he finishes in twelve this time.