Question

the event “A and union B” consists of all of the outcomes in both of the events

QUESTION 2 It has been reported that the proportion of Netflix subscribers has increased in the past year. A recent s reported that 27% of US Households have a subscription to Netflix instead of Showtime, HBO, or Star You decide to survey your neighborhood street, which is made up of 13 households and wonder the probability that exactly 3 households subscribe to Netflix. Find P(x 3), the probability that exactly 3 households subscribe to Netflix. 0.24 0.52 0.18 0.29

Answer 1

Solution:

   We are given that: a 27% of US households havs a subscription to Netflix.

That is: p = probability of US households having subscription to Netflix = 0.27

n = sample size = 13 households.

We have to find: P(X = 3) =.............?

X = Number of US households having subscription to Netflix follows a Binomial probability distribution with parameters n = 13 and p = 0.27.

Formula:
$P(X=x) = _{n}C_{x}\times p^{x}\times q^{n-x}$

where

$_{n}C_{x}=\frac{n!}{x!\times (n-x)!}$

and q = 1 - p = 1 - 0.27 = 0.73

Thus

$P(X=3) = _{13}C_{3} \times 0.27^{3} \times 0.73^{13-3}$

$P(X=3) = \frac{13!}{3!\times (13-3)!} \times 0.019683 \times 0.73^{10}$

$P(X=3) = \frac{13!}{3!\times 10!} \times 0.019683 \times 0.042976$

$P(X=3) = \frac{13 \times 12 \times 11 \times 10!}{3 \times 2 \times 1 \times 10!} \times 0.019683 \times 0.042976$

P(X = 3)--× 0.019683 × 0.042976 6

$P(X=3) =286 \times 0.019683 \times 0.042976$

Thus correct option is First Option.   0.24