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?

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

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.

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!