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A fair 6-sided die is rolled and you note whether the number facing up is even or odd. If an even number is rolled then a fair coin is flipped three more times and the number of heads is noted. But if an odd number is rolled then the coin is flipped only twice more and the number of tails is noted.

How many possible outcomes are there for this experiment?

(a) 43 (b) 20 (c) 7 (d) 45 (e) 18 (f) 36 (g) 71 (h) None of the above.

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Answer:

(f) 36

Step-by-step explanation:

There are 3 even and 3 odd numbers on a die.

For each even number, a coin is flipped 3 times. A coin has a head or a tail. Hence the number of possible outcomes for 3 flip of coins is [tex]2^3=8[/tex]. The number of possible outcomes for an even number on the die is 3 × 8 = 24

For each odd number, the coin is flipped 2 times, yielding [tex]2^2=4[/tex] possible outcomes for the coin and 4 × 3 = 12 possible outcomes for an odd number on the coin.

Hence, total number of possible outcomes = 24 + 12 = 36

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