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A coin 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?

Respuesta :

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)

[tex] x_1,\ x_2,\ x_3\ x_4,\quad x_i \in \{H,\ T\} [/tex]

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:

[tex] x_1,\ x_2,\quad x_i \in \{H,\ T\} [/tex]

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

fichoh

The number of possible outcomes in the sample space is 20.

Let:

Head = H

Tail = T

[tex]k^{n}[/tex]

Where;

k = number of outcomes per flip

n = number flips

If :

Head, H ;

4 more flips ; n = 4 ; k = 2

Sample space = [tex]2^{4}[/tex]

Sample space = 2 × 2 × 2 × 2 = 16

If ;

Tail, T ;

2 more flips ; n = 2 ; k = 2

Sample space = [tex]2^{2}[/tex]

Sample space = 2 × 2 = 4

Total sample space = 16 + 4 = 20 possible samples.

Learn more : https://brainly.com/question/18153040

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