What is the probability of getting 2 heads when tossing a coin 4 times?

Question

Pascal's triangle can be used.

Answer 1

6/16=3/8

Answer 2

ALL of the possibilities are (using a 1 for heads, and a 0 for tails) are:

0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

(Gee, it looks a lot like counting 0 to 15 in binary!)

16 possibilities. There are 6 of them with only 2 heads. 6/16=3/8 as already stated.

However, different ways of saying it get different results.10/16ths have at least 2 heads (5/8), 8/16 have at least 2 heads in a row, 4/16 have only 2 heads in a row, etc.

Another way to chart it is:
4 heads
3 heads, 1 tail
2 heads, 2 tails
1 head, 3 tails
4 tails

In this chart, where the order of the coins does not matter, it appears that the odds of at least 2 tails is 3/5, and of exactly 2 tails is 1/5. This chart is misleading, however, because it does not take into account the number of combinations for each group. That is, there are only one way for the first and last option to appear, 6 ways for 2 heads only to appear, and 4 ways each for the 3/1 ratio to show up (and 2+6+4+4=16 again!)

Finally, you can try it in real life. Flip 4 coins at a time and see how they come up, then chart the results. After a BUNCH of flips (aim for at least 160 tries), you should see the same basic results described.

Answer 3

I did the Pascal tree or triangle and the conclusion to get 2 heads (at least) is:

11/16 = 69%

Answer 4

Firstly, make a chart of coin flips going out to four times.
You should get something like this although it is kind of difficult to show over a computer:
4.)tails
3.)Tails
4.)Heads
2.)Heads
4.)Tails
3.)Heads
4.)Heads
1.)Heads
4.)Tails
3.)Heads
4.)Heads
2.)Tails
4.)tails
3.)Tails
Heads
1 flip = 1 2nd flip = 2 3rd flip = 3 4th flip = 4
4.)tails
3.)tails
4.)Heads
2.) Heads
4.)Tails
3.)Heads
4.)Heads
1.)Tails
4.)tails
3.)Heads
4.)Heads
2.)Tails
4.)tails
3.)Tails
4.)Heads


And if you look over you see that in 6 of the 16 outcomes you have heads only twice. but if you're looking for 2 times or more when heads shows up, the probability is 11 out of 16 trials where that occurs.
Hope that helps.

yahoo doesn't allow me to properly make out the diagram, but if you were to make a diagram like this on a piece of paper and you were to put the sides of the coins in their proper order, it would make more sense, sry.

Answer 5

1/2

Answer 6

If you mean exactly 2 heads, the probabiliy is 3/8.

Unless we use the magic coin I got in my pocket.

Answer 7

You have to ask the question correctly. Do you mean exactly 2 heads or at least 2 heads?

Answer 8

This is a binomial distribution problem:
k=2 successes, n=4 trials,
p=probability of success =.5,
q=probability of failure =.5

=(nCk)*(p^k)*(q^(n-k))

P(k=2 successes out of n=4) =

(4C2)(.5^2)(.5^2)=
6*.25*.25=.375

Answer 9

independant action 2 side = 50%
each chance is %50
Some might say the probability is 50x4/2=100%
But it is still %50 every time you flip it.