Question

PLEASE HELP ASAP

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.

Answer 1

PLEASE HELP
WILL BE FAN AND GIVE MEDAL

Answer 2

Let PI be the probability that Isabelle will win, and let PH be the probability that Heather will win. If we find the probability that Heather will win, the probability that Isabelle will win is found as follows:
\[\large P _{I}=1-P _{H}\ ...........(1)\]
For Heather to win she must gain four consecutive points. Therefore we can write:
\[\large P _{H}=(\frac{2}{3})^{4}\]
Plugging in the value of PH into equation (1) we get:
\[\large P _{I}=1-(\frac{2}{3})^{4}=you\ can\ calculate\]

Answer 3

Thank you!!

Answer 4

You're welcome :)