contestada

6. The television show Pretty Betty has been successful for many years. That show recently had a share of 23, meaning that among the TV sets in use, 23% were tuned to Pretty Betty. Assume that an advertiser wants to verify that 23% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a Pretty Betty broadcast. Find the probability that at least one of the households is tuned to Pretty Betty.
P(at least one)=

Respuesta :

jushmk
From the information given;
n = 11
p = 23% = 0.23
q = 1-p = 1-0.23 = 0.77

By binomial expression;
P_n(k,p)= (nCk)*(p)^k(q)^(n-k)

Then,
Probability that none of the household will be watching the TV is;
P(k=0) = (11C0)*(0.23)^0(0.77)^11 = 0.0564

Probability that one household will be watching TV is;
P(k=1) = (11C1)*(0.23)^1(0.77)^10 = 0.1854

Therefore, the probability that atleast one household will be watching TV is;
P(k≥1) = 1- [P(k=0)+P(k=1)] = 1-[0.0564+0.1854] = 0.7582