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anondriap
01.10.2019 •
Mathematics
Acasino wants to offer a new game with (potentially) spectacular prizes: the player flips a fair coin until they flip heads.the starting prize is \$2$2 (if the player flips heads on the first flip).the prize doubles with each flip after the first.for example, if somebody flipped tails-tails-tails-heads, then their prize would be \$16$16 (\$2($2 doubled three in other words, the prize is \$2^n,$2 n , where nn is the number of flips it took for the player to flip heads for the first time.how much should the casino charge to play this game?
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Ответ:
The casino should charge for this game at least $1 to break even.
Step-by-step explanation:
We can define the prize function as
where M is the prize money and n is the number of tails in continous flips.
The probability of n consecutive tails can be calculated as
. The probaility of getting a head after the n consecutive tails is
, so the probability of having n consecutive tails and a head is ![p^{n+1}=0.5^{n+1}](/tpl/images/0278/6900/8b195.png)
Then we can calculate the expected value of M as
The expected money prize for this game is $1, so the casino should charge to play at least $1 to break even.
Ответ:
D
Step-by-step explanation:
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