This could be solved by using the formula for Repeated Trials Probability:
[tex]Probability=(nCr)( p^{r} )( q^{n-r} )[/tex]
where
nCr is a combination formula: [tex] \frac{n!}{r!(n-r)!} [/tex]
But this can be easily solved using scientific calculator by inputing nCr.
n is the number of trials or total events (n=8)
r is the number of success trials or success out of the total events (r=4)
p is the probability of the success happening (p=46%)
q is the probability of the fail happening (q = 100-46%=54%)
Substituting,
[tex]Probability=(8C4)( 0.46^{4} )( 0.54^{8-4} )=0.2665[/tex]
Or in percentage form, the probability is 26.65%.
