1.Calculate the probability that Marieke wins

2. does anything change the results if Stef started

- Thread starter annasilva3
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1.Calculate the probability that Marieke wins

2. does anything change the results if Stef started

I dont knowI would start this by drawing a probability tree and seeing what it reveals. Do you know how to do that?

MP - Marieke plays

MW - Marieke wins

SP - Stef plays

SW - Stef wins

Now figure out the probability of each path through the (infinite) tree that leads to MW and sum them all.

For #2 do the same thing but have start go to SP instead of MP

Is it right that if Stef begins, the chance that Marieke can win is the same . (= 6/7)I really don't understand how you never learned how to draw a probability tree.

View attachment 11098

MP - Marieke plays

MW - Marieke wins

SP - Stef plays

SW - Stef wins

Now figure out the probability of each path through the (infinite) tree that leads to MW and sum them all.

For #2 do the same thing but have start go to SP instead of MP

Not quite. You did get the correct probability that Marieke wins though.Is it right that if Stef begins, the chance that Marieke can win is the same . (= 6/7)

Isn't it just 1/2 * (1/ (1-(5/6)*(1/2)))Not quite. You did get the correct probability that Marieke wins though.

\(\displaystyle p[MW] = \dfrac 5 6 \dfrac 1 2 + \dfrac{5}{6} \left(\dfrac{5}{12}\right)\dfrac 1 2 + \dfrac{5}{6} \left(\dfrac{5}{12}\right)^2 \dfrac 1 2 + \dots + \dfrac{5}{12} \left(\dfrac{5}{12}\right)^k + \dots= \\

\dfrac{5}{12}\sum \limits_{k=0}^\infty \left(\dfrac{5}{12}\right)^k = \dfrac{5}{12} \cdot \dfrac{12}{7} = \dfrac 5 7\)

Thank u

\(\displaystyle p[MW] = \dfrac 5 6 \dfrac 1 2 + \dfrac{5}{6} \left(\dfrac{5}{12}\right)\dfrac 1 2 + \dfrac{5}{6} \left(\dfrac{5}{12}\right)^2 \dfrac 1 2 + \dots + \dfrac{5}{12} \left(\dfrac{5}{12}\right)^k + \dots= \\

\dfrac{5}{12}\sum \limits_{k=0}^\infty \left(\dfrac{5}{12}\right)^k = \dfrac{5}{12} \cdot \dfrac{12}{7} = \dfrac 5 7\)