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Give an example that shows the second condition in the multiplication principle (that composite outcomes are...

Give an example that shows the second condition in the multiplication principle (that composite outcomes are distinct) is required in order to obtain the correct count.

Math   Statistics-And-Probability   
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Answer #1

Solution: If a composite outcome can be described by a procedure that can be divided into k successive stages.

I.e, n1 outcomes in stage 1, n2 in stage 2..........nk in stage k.

If the number of outcomes in each stage is independent of the choices in previous stage and all the outcomes are distinct, then the number of possible composite outcomes =n1*n2*.......nk.

For example, Suppose the composite outcomes of a bike is denoted by M1 and M2 are two mileage classes and P1, P2 and P3 are three price classes.

There are two stages of outcomes.

Stage 1: Two outcomes in mileage class( M1 and M2)

Stage 2: Three outcomes in price class( P1, P2 and P3)

Here the number of outcomes in both the cases are independent.

Therefore, there will be 2*3=6 distinct composite outcomes.

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