Question

The probability that a randomly selected teenager watched a rented video at least once during a week was 0.75. What is the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week? (Round your answer to four decimal places.)

Answer 1

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,

$P(x)=^nC_x p^x q^{n-x}$

Where,

$^nC_x=\frac{n!}{x!(n-x)!}$

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)

$=^7C_5 0.75^5 0.25^{7-5}+^7C_6 0.75^6 0.25^{7-6}+^7C_7 0.75^7 0.25^{7-7}$

$=21 (0.75)^5 (0.25)^2 + 7 (0.75)^6 0.25 + 0.75^7$

$=0.756408691406$

$\approx 0.7564$