Make a table showing the probability distribution for the possible number of heads when tossing 5 coins...

Question

Make a table showing the probability distribution for the possible number of heads when tossing 5 coins.

(Give the probabilities as decimals rounded to five decimal places.)

# of heads   Probability
0                 ?
1                 ?
2                 ?
3                 ?
4                 ?
5                 ?

Answer 1

Emily,

  Here is the answer to a similar problem:

https://www.wyzant.com/resources/answers/223137/my_question_is_in_the_description

 

For your problem we have p=q=1/2,

and you want the case for n=5 which is given by:

 

1 = (p+q)⁵ = 1p⁵ + 5p⁴q + 10p³q² + 10p²q³ + 5pq⁴ + 1q⁵

 

Because p=q=1/2, the pq parts of all of these terms are all the same: (1/2)⁵ = 1/32, so we have:

1 =   (1 + 5 + 10 + 10 + 5 + 1) /32

The 6 different terms give the probabilites for 5 heads, 4 heads, ..., one head, zero heads.

In a table:

 

heads Probability
0     1/32
1     5/32
2   10/32
3   10/32
4     5/32
5     1/32

 

You can use a calculator to do the divisions and round each of them to 5 decimal places.