# Probability Problems

1) A very rich investor has a small amount of spare cash which she wishes to invest. She has four options to choose from. She thinks company 1 has a 43% chance of giving her a return of $327, otherwise she believes it will lose her $296. She thinks company 2 has a 81% chance of giving her a return of $228, otherwise she believes it will lose her $1043. She thinks company 3 has a 46% chance of giving her a return of $181, otherwise she believes it will lose her $187. She thinks company 4 has a 33% chance of giving her a return of $705, otherwise she believes it will lose her $205. Based on these opinions, which company should she invest in?

2) In a certain mining town there are 3 times as many men as women. 64% of the men and 28% of the women attend the weekly football match. During half time a ticket is selected and the holder of that ticket is selected to win a prize. What is the probability that the holder of the winning ticket is a woman?

© BrainMass Inc. brainmass.com October 24, 2018, 6:47 pm ad1c9bdddfhttps://brainmass.com/engineering/mining-engineering/probability-problems-48936

#### Solution Preview

1) Need to use the formula for calculating expected return:

EXPECTED RETURN = POTENTIAL RETURN* PROBABILITY OF ...

#### Solution Summary

The solution provides a detailed and step-by-step explanation (incl. Excel calculations) for the problem.

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?