Acoin is flipped. if a heads is flipped, then the coin is flipped 4 more times and the number of heads flipped is noted; otherwise (i. e., a tails is flipped on the initial flip), then the coin is flipped 2 more times and the result of each flip (i. e., heads or tails) is noted successively. how many possible outcomes are in the sample space of this experiment?

The first flip can obviously return only H or T.

Suppose the coin lands on H. This means that every following string is possible (and thus part of the sample space)

So, there are 16 such strings, because every flip has two possible outcomes.

Suppose now the coin lands on T. Like before, we add to the sample space the following strings:

And thus there are 4 such strings, because we have two choices for each of the two flips.

So, the sample space has 20 outcomes:

H - HHHH

H - HHHT

H - HHTH

H - HHTT

H - HTHH

H - HTHT

H - HTTH

H - HTTT

H - THHH

H - THHT

H - THTH

H - THTT

H - TTHH

H - TTHT

H - TTTH

H - TTTT

T - HH

T - HT

T - TH

T - TT

5 + 8 +7 + 4 + 0 +1 = 25

step-by-step explanation: