From Randomness to Probability

1
Chapter 14

• From Randomness to Probability

2
Law of Large Numbers

• Probability ? Long-run relative frequency.
• Probability refers to our knowledge of how things
  behave in the long run, even though we cant
  predict individual outcomes
• ActivStats tool

3
Illustrative Example
4
12 and 14 Stats projects

• In a large Intro Stats class, the professor
  reports that 55 have never take a Calc course,
  32 have take only 1 semester Calc, the rest have
  taken 2 semesters. The professor randomly
  assigned groups of 3 for a project.
• What is the probability that your first groupmate
  has studied.
• 2 or more semesters of Calc?
• Some calc?
• No more than one semester of calc?
• Of your 2 groupmates, what is the probability
  that.
• Neither has studied Calc?
• Both have studied at least one semester of Calc?
• At least one has had more than 1 semester of Calc?

5
24 Blood

• 45 of US has Type 0, 40 has A, 11 has B, rest
  have AB.
• What is probability that a single donor has
• Type AB?
• Type A or Type B?
• Not Type O?
• What is the probability that with 4 donors
• All are type O?
• No one is type AB?
• They are not all type A?
• At least one is type B?