Heather and isabelle play a two-person game which is won by the first person to accumulate 10 points. at each turn heather gains a point with probability of 2/3. if she doesn't get a point then isabelle gets a point. isabelle is now ahead 9 to 6. what is the probability that isabelle will win? express your answer as a common fraction.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

do a bckflip awfwgawgawggw

okay, what do you want us to do?

step-by-step explanation: