Binomial Distributions

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Presentation transcript:

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

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: