1.4.3 Calculating Combinatorial Probabilities

Question 1

What are the two steps in calculating combinatorial probabilities?

Answer 1

(1) Count the favorable outcomes; (2) Divide by the total number of equally likely outcomes.

Question 2

What is the general formula for combinatorial probability?

Answer 2

P = (# of desired outcomes) / (# of total possible outcomes)

Question 3

In sampling without replacement, what are the two valid approaches?

Answer 3

You can solve assuming (1) order matters, or (2) order does not matter — as long as you’re consistent.

Question 4

In sampling with replacement, do you consider order?

Answer 4

Yes — generally you must consider order because the pool doesn’t change.

Question 5

Can you switch between permutations and combinations mid-problem?

Answer 5

No. Be consistent — use the same assumption for both numerator and denominator.