If you toss a fair coin three times, what is the probability of tossing exactly two heads?

Question

I know the answer to this problemis 3/8. I just don't know how they came up with it. Can anyone help. I figured if you multiplied the answer should have been 1/8????

Answer 1

You could have
HHT or HTH or THH so you have 3 possibilites of getting exactly 2 heads
There are 2^3 = 8 total possibilites.
Answer: 3/8

Answer 2

Sure.

The probability of tossing a coin and getting heads or tails is 1/2.

You are going to toss the coin 3 times.

1/2 x 1/2 x 1/2 = 1/8.

Now, you want two heads in a row.

This can occur as follows:

Tails/Heads/Heads

or

Heads/Heads/Tails.

or

Heads / Tails / Heads.

This is a long way to explain it, but there are exactly 3 ways (out of eight) that a coin thrown three times will give two heads.

3 x (1/8) =

3/8

The other five ways: Tails/Tails/Tails Tails/Tails/Heads etc will not give two heads.

Regards,

Mysstere

Answer 3

The sample space looks like this:
HHH, HHT, HTH, THH, HTT, THT, TTH, TTT

The probability of each outcome is 1/8. Exactly 2 heads can occur 3 ways so you figure the probability by adding
1/8 + 1/8 + 1/8 = 3/8

Answer 4

Ask this: which scenarios give you exactly 2 heads? There are 3: heads,heads,tails; heads,tails,heads; tails,heads,heads.

There are 2^3=8 possibilities altogether, because each coin flip has 2 outcomes, and there 3 flips.

Therefore, the probability of exactly 2 heads is

(# scenarios with exactly 2 heads) / (# total scenarios) = 3/8.

Answer 5

from binomial expansion
1,3,3,1 total=8
or
all 3 heads=1/8
2 heads & 1 tail=3/8
1 head & 2 tails=3/8
all 3 tails=1/8

total: 1/8+3/8+3/8+1/8=8/8=1

Answer 6

easiest way is to "make a list"

T T T
T T H
T H T
T H H <===
H T T
H T H <===
H H T <===
H H H

and "count" the number of times 2 H's appear
and you get "3" ... and the number of rows in
the list = 8

probability = 3/8

this is how probability is defined ...
formulas can come later, but without understanding
of the counting principle, they are of limited use.
((unless you enjoy memorization of massive
amounts of confusing details which you would
also need to memorize,... and "apply correctly" ))

... nahhh,
make a list and 'generalize' from it if you need to

you will have a MUCH higher probability of
being correct using this method.

I know