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# Probability problems

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7. Let A(4,3) and B(7,11) be two points in a plane.
If all paths are equally likely, what would be the probability of choosing a path that begins with an up move and ends with an up move? (Each path is made up of moves that either go up one unit or over one unit to the right.)

8. In a state lottery game, anyone who picks 6 numbers out of 36 wins \$50,000, no matter how many people correctly guessed the winning numbers. What are the odds of winning in this game?

HINT:
You are picking 6 numbers from 36. No order is specified and you cannot pick the same number twice.

9. The first three characters of a car license plate number are letter characters.
Car license plates can have repeats. For a), remember that the combination "AA" is possible.

a) Whatâ??s the probability of the first three characters being BAZ?
b) Whatâ??s the probability of the second character being K?
c) Whatâ??s the probability that the first character is either A, B, or C?

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#### Solution Preview

7. The total number of possibilities is 11 combined three at a time or 165 and there are 9 of them that move up at the beginning and at the end. So the odds are 9:156 or 3:52.
There has to be eleven total moves, 3 going up and 8 going right. So think of it as 11 blanks and you are trying to figure out where the 3 'ups' ...

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## Three questions on probability

1) Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:
a) What is the probability that the drug will be effective for 2 hours or less?
b) 1 hour or less?
c) 3 hours or more?

2) Life span for red foxes follow an approximately normal distribution with mean 7 years and standard deviation 3.5 years.
a) Find the probability that a red fox chosen at random will live at least 10 years.
b) Find the probability that a random sample of 4 red foxes will have a sample mean life span of over 10 years.

3) Margot has found that the mean time to run a job at the college copy center is 12.6 minutes with standard deviation 10 minutes. She selects a random sample of 64 jobs.
a) What is the probability that the sample mean copying time is between 14 and 15 minutes?
b) What is the probability that the sample mean copying time for this sample is between 10 and 12 minutes?

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