Help me understand: "Mark and Rory play a one-on-one basketball game in which the first who makes a basket wins...."

[nash013013]

Mark and Rory play a one-on-one basketball game in which the first who makes a basket wins. Mark is a much stronger rebounder than Rory and Mark will rebound any missed shot (by herself or Rory). After rebounding the ball, Mark systematically dribbles back to the three-point line before shooting. Rory can only regain and steal the ball when Mark dribbles. Both shoot the ball equally well and have a 40% probability to make any shoot they attempt. In order to determine who has the first possession, Mark and Rory flip a coin.

Let p be the probability of Rory stealing the ball. What value should p take so that Mark has a 70% chance to win the game before the coin is flipped? Justify your answer mathematically. Be sure to note what probability concept/equation is utilized.


So I keep getting a negative answer of -0.25, and idk what i am doing wrong since the probability cant be negative. Can someone help me?

 

[stapel]

Mark and Rory play a one-on-one basketball game in which the first who makes a basket wins. Mark is a much stronger rebounder than Rory and Mark will rebound any missed shot (by herself or Rory). After rebounding the ball, Mark systematically dribbles back to the three-point line before shooting. Rory can only regain and steal the ball when Mark dribbles. Both shoot the ball equally well and have a 40% probability to make any shoot they attempt. In order to determine who has the first possession, Mark and Rory flip a coin.

Let p be the probability of Rory stealing the ball. What value should p take so that Mark has a 70% chance to win the game before the coin is flipped? Justify your answer mathematically. Be sure to note what probability concept/equation is utilized.


So I keep getting a negative answer of -0.25, and idk what i am doing wrong since the probability cant be negative. Can someone help me?

Please reply *showing* your work and reasoning, so we can try to figure out what's going wrong. Thank you!

 

[nash013013]

So, i set up some values for equations
M-Probability that Mark maskes a shot(40%)
R-Probability that Rory makes a shot(40%)
P-Probability that Rory steals the ball
Q-Probability that Mark rebounds a ball and eventually makes a shot
W-Probability that Mark wins the game
And so I figured that I would get the equation below
W=M+(1-R)*(1-P)*M
And since W has the probability of 70% or 0.7 and M and R have the probability of 40% or 0.4, i input the numbers and get
0.7=0.4+(1-0.4)(1-P)0.4
Which, when solved for P gives me the answer of -0.25

 

[Steven G]

I might be wrong, but I don't see where you took into the result for the flip of the coin. Maybe you think that doesn't matter?