Answer:
The theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.
Step-by-step explanation:
Getting x successes out of n trials is a binomial distribution and is given by:
p(x) = [tex]nC_{x} p^{n-x} q^{x}[/tex]
Here, n = 6
x = 2
p = probability of one head = [tex]\frac{1}{2}[/tex]
q = 1 - p
= [tex]1-\frac{1}{2}[/tex]
= [tex]\frac{1}{2}[/tex]
Substitute these values, we get,
p(2) = [tex]6C_{2} (\frac{1}{2} )^{6-2} (\frac{1}{2} )^{2}[/tex]
= [tex]15(\frac{1}{2} )^{6}[/tex]
= [tex]\frac{15}{64}[/tex]
= 0.234
= 23.4%
We know that [tex]6C_{2} =6C_{6-2}[/tex]
[tex]6C_{2} =6C_{4}[/tex]
Now,
p(4) = [tex]6C_{4} (\frac{1}{2} )^{6-4} (\frac{1}{2} )^{4}[/tex]
= [tex]15(\frac{1}{2} )^{6}[/tex]
= p(2)
Hence, the theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.
