Homework 1 Questions

1. An outfit consists of 1 shirt, 1 pair of pant, 1 jacket, and 1 pair of shoes. Suppose you are tasked with picking one outfit. You have 5 shirts, 7 pairs of pants, 3 jackets, and 10 pairs of shoes to choose from. What is the sample space for this experiment and the number of outcomes in the sample space?

2. If 21 one-armed people attend a party, how many different handshakes can occur?

3. A group of 19 people is formed into two lines: Line 1 has 12 people and Line 2 has 7. How many unique ways can this occur?

4. A dance class has 13 men and 17 women. How many different ways can 6 men and 6 women be chosen and then paired together in man+woman pairs?

5. A group of people is asked if they like coffee, tea, both, or neither. Suppose

• 67% like coffee,

• 56% like tea, and

• 61% either dont like tea or dont like coffee.

What percentage of people like neither?

6. Suppose you are monitoring a group of people divided into three categories: Young/Old, Smoker/Nonsmoker, Male/Female. You know the following information:

• 75% are Young

• 60% are Smokers

• 42% are Male

• 48% are Young Smokers

• 23% are Young Males

• 31% are Male Smokers

• 6% are Young Male Smokers

What percentage are Old Female Nonsmokers?

7. A species of bird has only either red or blue feathers. You know that 60% of the species is female and 40% of the species is male. If you estimate that 33% of all birds are red-feathered and female, what percentage of female birds have red feathers?

8. Suppose a healthcare policy is purchased for a group of 900 people of varying ages.

   • 180 are "18 - 25",

   • 470 are "26 - 39" and

   • The remaining 250 are "40+".

It is also known that the following percentages of the three age groups will file more than one claim:

8. • 8% of 18 - 25 year olds

   • 13% of 26 - 39 year olds

   • 22% of 40+ year olds

What is the probability that a randomly selected person from this group files more than one claim?

9. A species of rabbits can have either blue or brown eyes, and either white or grey fur. Suppose you know the following information:

   • 87% of the rabbits have grey fur.

   • 73% of rabbits with white fur have blue eyes

   • 81% of rabbits with grey fur have brown eyes.

What is the probability that a blue-eyed rabbit will have white fur?

10. Suppose you administer a test for presence of a certain toxin in a persons bloodstream. You know this toxin is only present in 0.4% of the total population. From previous trials you make the following estimates:

    • If someone has the toxin, the test returns positive 99% of the time.

    • If someone does not have the toxin, the rest returns positive 0.1% of the time.

What is the precision of the test, i.e. the probability that someone with a positive test has the toxin present in their blood?