Question

i need help with probabilities
A foreign student club lists as its members 2 Canadians, 3 Japanese, 5 Italians, and 2 Germans. If a committee of 4 is selected at random, find the probability that all nationalities except the Italians are represented

Answer 1

The total number of students is 12, so to find the probability we'll do the following
for the Canadians the probability is 2/12 for the next Japanese member 3/11 for the german member 2/10 and for the last member 4/9 as there are only 4 non italian members left multiplying the probabilities
2/12*3/11*2/10*4/9=0,00404=0,404%

Answer 2

P(all nationalities except the Italians are represented) = 7C4/12C4

Answer 3

Canadians Japanese Germans Italians
(A) 1 1 2 0
(B) 1 2 1 0
(C) 2 1 1 0
The possible combinations are shown above.
\[\large P(A)=\frac{2C1\times3C1\times2C2\times5C0}{12C4}=\frac{6}{495}\]
\[\large P(B)=\frac{2C1\times3C2\times2C1\times5C0}{12C4}=\frac{12}{495}\]
\[\large P(C)=\frac{2C2\times3C1\times2C1\times5C0}{12C4}=\frac{6}{495}\]
The events A, B and C are mutually exclusive. Therefore the probability that all nationalities except the Italians are represented is:
\[\large P(A)+P(B)+P(C)=\frac{6}{495}+\frac{12}{495}+\frac{6}{495}=\frac{24}{495}=0.0485\]

Answer 4

Thank you so much, I passed my statistics class because of this, sorry for the late credit :))

Answer 5

That you for the feedback. Congratulations for your result :)