Mr. adams and ms. smith are betting on repeated flips of a coin. at the start of the game mr. adams has a dollars and ms. smith has b dollars, at each flip the loser pays the winner one dollar, and the game continues until either player is “ruined.” making use of the fact that in an equitable game each player’s mathematical expectation is zero, find the probability that mr. adams will win ms. smith’s b dollars before he loses his a dollars.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

11

step-by-step explanation:

32.50-7.50=25

225/25=11

p

step-by-step explanation:

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