Answer:
0.7564
Step-by-step explanation:
Let X be the event of watching a rented video at least once during a week,
Given,
The probability of watching a rented video at least once during a week was, p = 0.75,
So, the probability of not watching a rented video at least once during a week was, q = 1 - p = 0.25,
Binomial distributive formula,
[tex]P(x)=^nC_x p^x q^{n-x}[/tex]
Where,
[tex]^nC_x=\frac{n!}{x!(n-x)!}[/tex]
Hence, the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week,
P(X ≥ 5) = P(X=5) + P(X=6 )+ P(X=7)
[tex]=^7C_5 0.75^5 0.25^{7-5}+^7C_6 0.75^6 0.25^{7-6}+^7C_7 0.75^7 0.25^{7-7}[/tex]
[tex]=21 (0.75)^5 (0.25)^2 + 7 (0.75)^6 0.25 + 0.75^7[/tex]
[tex]=0.756408691406[/tex]
[tex]\approx 0.7564[/tex]
