A few days ago
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# Probability Problem?

Consider the experiment of flipping a fair coin four times and counting the number of heads.

A few days ago
David J

0h – 1 sequence

1h – 4 sequences.

2h – 6 sequences.

3h – 4 sequences.

4h – 1 sequence.

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A few days ago
j.investi
hmm.. flipping a fair coin four times. Say, H is for head and T is for tail, then the (all) possible outcomes are:

(H, H, H, H), (H, H, H, T), (H, H, T, H), (H, H, T, T), …, (T, T, T, T)

(there are 2^4 = 16 possible outcomes. More generally, if you flip a fair coin n times, then the number of all possible outcomes is 2^n).

I usually just list all the possible outcomes.. It’s only 16 anyway 🙂

and to get the probability… e.g. the probability of 1-head outcomes is:

1. list of the 1-head outcomes: (H, T, T, T), (T, H, T, T), (T, T, H, T), (T, T, T, H).

2. the probability = Pr(1 head) = 4 / 16 = .25

use the same process to find the probability of the other kind of outcomes. 🙂

0

A few days ago
Wai Choong Shum
The sequence with no head = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

The sequence with exactly 1 head = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

The sequence with exactly 2 head = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

The sequence with exactly 3 head = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

The sequence with 4 heads = 1/2 * 1/2 * 1/2 * 1/2 = 1/16

0

A few days ago
bipolarbear23
There are 16 possible outcomes from flipping four fair coins

1 head = 4/16 HTTT, THTT, TTHT, TTTH

2 heads = 6/16 HHTT, HTHT, HTTH, THHT, THTH, TTHH

3 heads = 4/16 HHHT, HHTH, HTHH, THHH

0

A few days ago
gerald M
I don’t believe this is a probability problem. Since each flip of the coin is a new test, the flipping of the coin, height, spin, etc are factors onto their own and do not make up a sequence.
0

A few days ago
Soon To Be Famous!