Respuesta :
Answer:
0.234
Step-by-step explanation:
Given : You flip a fair coin 6 times
To Find: What is the probability that you will get exactly 4 tails
Solution:
Formula : [tex]P(X=r) =^nC_r p^r q^{n-r}[/tex]
Where r is the no. of success
n is the total no. of trials
p is the probability of success
q is the probability of failure
In This case success is getting tail
So, Probability of getting tail = [tex]\frac{1}{2}[/tex]
So, Probability of not getting tail = [tex]\frac{1}{2}[/tex]
n = 6
r = 4
[tex]p =\frac{1}{2}[/tex]
[tex]q=\frac{1}{2}[/tex]
Substitute the values in the formula
[tex]P(X=4) =^6C_4 (\frac{1}{2})^4 (\frac{1}{2})^{6-4}[/tex]
[tex]P(X=4) =\frac{6!}{4!(6-4)!}(\frac{1}{2})^4 (\frac{1}{2})^{2}[/tex]
[tex]P(X=4) =0.234[/tex]
Hence the probability that you will get exactly 4 tails is 0.234
