1 A coin is flipped once If the result is a heads the coin i

1/ A coin is flipped once. If the result is a heads, the coin is flipped 2 more times, and the result (heads or tails) of each successive flip is noted. If the result is a tails, the coin is flipped 4 more times and the result of each successive flip is noted.

How many possible outcomes are in the sample space of this experiment?

Solution

1.

From the first toss, there are 2 possibilities.

1H, 1T.

If we have heads, the coin if slipped 2 more times. That will yield 2*2 = 4 possibilities.

If we have tails, the coin is flipped 4 more times. That will yield 2*2*2*2 = 16 possibilties.

Thus, that will in total have 4 + 16 = 20 outcomes. [ANSWER]

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2.

As it matters which student is assigned on an issue, then order matters.

Thus, we use permutations.

Hence, there are 14P4 = 24024 ways to assign. [ANSWER]