Question 843188: Billy and Betty are each flipping one coin. Billy flips his three times and Betty flips hers four times. How many possible outcomes are there for Billy? How many possible outcomes are there for Betty? If we consider this all one experiment in which Billy does his part first and then Betty does her part, how many possible outcomes are there altogether?
We know that the number of possible outcomes for Billy is 23 = 8 and the number of possible outcomes for Betty is 24 = 16.
The total number of outcomes for both is 27 = 128. Note that 23 × 24 = 8 × 16 = 128 = 27.
My question - I don't understand why the number of outcomes is multiplied rather than added. For example, with Billy, shouldn't his 3 flips = 6 possible outcomes, not 8? First outcome, H or T = 2; 2nd outcome, h or t = 2; 3rd outcome, h or t = 2; therefore 2+2+2=6. Please explain why 2x2x2.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Nope, independent outcomes are multiplied. For example, there are 2 ways for each of three flips, and 2^3 = 8 possibilities total:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
Can also be seen by drawing a tree.
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