Binomial

[Sue20]

Flip a fair coin 4 times. What is the probability of observong exactly three heads?
* Should I use binomialpdf or use the HHH method? Please Help!!

 

[srmichael]

I would use the binomial distribution formula. You want 3 heads each head with a probability of 0.5 of occurring....take it from here...

 

[pka]

Flip a fair coin 4 times. What is the probability of observong exactly three heads?

How many ways are there to arrange this string \(\displaystyle hhth~?\)
Then multiply that by \(\displaystyle (0.5)^4~.\)

 

[Sue20]

There are 4 ways so would you mulitply (0.5) (0.5) (0.5) (0.5)?

 

[pka]

There are 4 ways so would you mulitply (0.5) (0.5) (0.5) (0.5)?

You have missed to whole point!
There are four ways to arrange \(\displaystyle THHH\) and each arrangement has probability \(\displaystyle (0.5)^4\).
So what is the answer?

 

[Sue20]

binomial

Is it .25? .0625 x 4= .25

 

[pka]

Is it .25? .0625 x 4= .25

Correct.
If you toss a coin ten times the probability of exactly seven heads is
\(\displaystyle \dbinom{10}{7}(0.5)^{10}=\dfrac{10!}{7!\cdot 3!}(0.5)^{10}\)

If you toss a coin N times the probability of exactly \(\displaystyle 0\le K \le N\) heads is
\(\displaystyle \dbinom{N}{K}(0.5)^{N}=\dfrac{N!}{K!\cdot (N-K)!}(0.5)^{N}\)

 

[Sue20]

The problem states that you are looking for three heads