Probability Question, need help!?1. Two soccer teams, A and B, have a kick off to see which team wins the game. The team take turns to attempt to score a goal. The first team to score wins. The probability of team A winning with 1 kick is 0.20. The probability of team B winning with 1 kick is 0.25.
a) Suppose team A kicks first. What is the probability that team B wins on its first kick?
b) Suppose team A kicks first. What is the probability that team A wins on its third kick?
c) Suppose team A kicks first. What is the probability that team A wins?
d) Suppose team B kicks first. What is the probability that team B wins?
I got part a, but the rest...need some help. Can anyone explain it to me? I just want to see how you did it, you don't have to calculate the final answer. Thanks!
And also, if you could help me with this one...
2. A new medical test for glaucoma is 95% accurate. Suppose 0.8% of the population has glaucoma. What is the probability of each event?
a) A randomly selected person will test negative. (I got 94.24% but the answer is 94.28%)
b) A person who tests negative has glaucoma. (do not have to answer this one, I got it)
c) A person who tests positive does not have glaucoma. (NEED HELP on this one).
Thanks so much!
Posted by AD
1 b)
For A to win on the third kick, both teams have to miss twice, and then A has to score:
P = 0.8 * 0.75 * 0.8 * 0.75 * 0.2 = 0.072
For c) and d) I suppose you'll have to set up a sum to infinity, but I don't quite remember how to do those at the moment
2 a)
P(negative) = 0.95*0.992 + 0.05*0.008 = 0.9428
95% chance of accurately testing a person without plus 5% chance of incorrectly testing a person with glaucoma.
c)
Proportion of tests that are positive tests and person has glaucoma = 0.95 * 0.008 = 0.0076
Proportion of tests that are positive tests and person does not have glaucoma = 0.05* 0.992 = 0.0496
0.0496 / (0.0076 + 0.0496) = 0.0496 / 0.0572 = 0.867
P(does not have glaucoma if tested positive) = 0.867
I hope that last bit makes sense, not quite sure how to explain it better.
Orignal From: Probability Question, need help!?
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