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How do you find the probability of selecting a group of a certain composition (e.g. 3 soldiers, 2 sailors, 4 airmen, 1 Marine)?
Use the combination formula and the Fundamental Counting Principle
Numerator: C(total in category 1, number you need out of that category) x C(total in category 2, number you need out of that category) x ... x C(total in last category, number you need out of that category)
Denominator: C(total in all categories, size of the group you’re selecting)
How would you find the probability of selecting a certain number of rubber balls that are all the same color?
Decision 1: Which color?
Decision 2: Which balls of that color?
Multiply the total ways to make those choices (Fundamental Counting Principle). Make that the numerator.
Denominator: C(total balls, number of balls you want)
How would you find the probability of selecting a group of rubber balls where some are one color and some are another color?
Decision 1: Which color first?
Decision 3: Which color second? (How many colors left?)
Decision 4: Which balls of that color?
Multiply the number of ways to make each decision (Fundamental Counting Principle). Make that the numerator.
Denominator: C(total balls, number of balls you have to select)
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