Answer to Question #235857 in Statistics and Probability for WHY NOT

Question

 A Ghana Tourist Board survey for Ghana Travel & Tours Association asked respondents, "When traveling internationally, do you generally venture out on your own to experience culture, or sack with your tour group and itineraries?" The survey found that 23% of the respondents stick with their tour group.

i. In a sample of six internadonal travelers, what is the probability that two will sack with their tour group?

ii. In a sample of six internadonal travelers, what is the probability that at least Byo will stick vhth their tour group?

iii. In a sample of 10 intemadonal travelers, what is the probability that none will sack with the tour group?

Answer 1

Solution:

$p=23\%=0.23,q=1-0.23=0.77$

$X\sim Bin(n,p)$

(i) n=6

$P(X=2)=^6C_2(0.23)^2(0.77)^4=0.2789$

(ii) n=6

'At least Byo' is unclear, we assume 'at least one'.

$P(X\ge1)=1-P(X<1)=1-P(X=0)=1-^6C_0(0.23)^0(0.77)^6=$

$=1-0.20842 \\=0.79158$

(iii) n=10

$P(X=0)=^{10}C_0(0.23)^0(0.77)^{10}=0.07326$