1 in a trillion, I think not.

Check out this article on what could incorrectly be considered Bernoulli trials.

http://www.bbc.co.uk/news/magazine-16118149

Independence matters!

Ch 16 - What you should know.

Ch 17 Summary

You should know what a Bernoulli Trial is, and when doing a problem check for these  conditions (that means write out how you know it meets these conditions)

• There are two possible outcomes 
• The probability of success is constant
• The trials are independent (you can use the 10% condition if they are not truly independent)

You should know when to use a Geometric Probability model, geom(p).

• For a random variable that counts the number of Bernoulli Trials until the first success

You should know when to use a Binomial model, binom(n,p)

• For a random variable that counts the number of success in a fixed number of Bernoulli Trials. 

You should know about the success failure Condition

• For a Normal model to be a good approximation of a Binomial model, we must expect at least 10 success, and at least 10 failures. np>=10, and nq>= 10

Calculator skills

• geometpdf(p,x) returns the probability of an individual outcome
• geometcdf(p,x) returns the cumulative probability from 0 to x. Use for at least or at most problems.
• binompdf(n,p,X) returns the probability of an individual outcome
• binomcdf(n,p,X) returns the cumulative probability from 0 to X. Use this in At least situations, or at most situations. 

Here are some more problems to test your knowledge of Bernoulli trials, geometric and binomial probability models.

Ch 17 practice problems

Chapter 17 Guiding Questions

1) What is a Bernoulli Trial? What are the requirements for Bernoulli Trials?

2) What is a geometric probability model for Bernoulli trials? Explain and give the formulas for mean and standard deviation.

3) What is a binomial probability model for Bernoulli trials? Explain and give the formulas for mean and standard deviation.

4) What is the success/failure condition and when is it used with binomial models?

For the following questions: Tell me if this is a geometric or binomial model. Then solve the problem.

5) Assume that 13% of people are left handed. If we select 5 people at random, what is the probability that the first lefty is the fifth person chosen.

6) Assume that 13% of people are left handed. If we select 5 people at random, what is the probability that there are some lefties among the 5 people.

7) Assume that 13% of people are left handed. If we select 5 people at random, what is the probability that the first lefty is the second or third person.

8) Assume that 13% of people are left handed. If we select 5 people at random, what is the probability that there are exactly 3 lefties in the group.

9) Assume that 13% of people are left handed. If we select 5 people at random, what is the probability that there are at least 3 lefties in the group.

10) Assume that 13% of people are left handed. If we select 5 people at random, what is the probability that there are no more than 3 lefties in the group.