Binomial Distributions

Permutations & Combinations• nPk = Finds number of Possibilities when

picking k individuals out of a group of size n– Order Matters– Can Only Pick Each Individual Once

• nCk = Finds number of Possibilities when picking k individuals out of a group of size n– Order Doesn’t Matter– Can Only Pick Each Individual Once

Binomial Distribution AKA BINS

Calculates the odds of succeeding X times after trying Y times given certain constraints

Binomial Distribution

4 Conditions to be a Binomial Distribution: BINS• Binary? Can you define each trial so that there

are only two possible outcomes: success or failure?

• Independent? The outcome of each trial needs to be independent of the previous trials (order doesn’t matter)

• Number? The number of trials needs to be predetermined. Can’t do I’ll draw cards until I get an Ace. Has to be I’ll draw 5 cards.

Binomial Distribution

4 Conditions to be a Binomial Distribution: BINS• Binary?• Independent? • Number? The number of trials, n, needs to be

predetermined. Can’t do I’ll draw cards until I get an Ace. Has to be I’ll draw 5 cards.

• Success? On each trial, the probability, p, of success must be the same

Binomial Distribution

4 Conditions to be a Binomial Distribution: BINS• Binary?• Independent? • Number? • Success? • Page 401, Example 8.12• Page 402, Example 8.13

Binomial Theorem

• In a binomial setting involving n independent trials with each having a probability p of success, the probability of getting exactly k successes is given by: