Question

In a particular suburb of Melbourne, 50% of the inhabitants speak English as a first language, 20% speak Chinese, 15% Greek, 10% Polish, and 5% any other language. At the entrance of the local shopping centre, somebody is asking ten random people a number of questions. Calculate the probability that: • Two of these people speak Polish and two speak Greek as a first language. Three of these ten people speak Chinese as a first language. At least four of these ten people speak English as a first language. At most two of these ten people speak Chinese as a first language. • •

Answer 1

1)P(2 polish 2 greek and rest 6 other ) =(10!/(2!*2!*6!))*(0.1)²*(0.15)²*(0.75)⁶=0.0505

2)

here this is binomial with parameter n=10 and p=0.2

probability =

P(X=3)=

(10C3)0.23(1−0.2)(7)    =

0.2013

3)

this is binomial with parameter n=10 and p=0.5

probability =

P(X>=4)=

1-P(X<=3)=

1-∑x=0x-1     (nCx)px(1−p)(n-x)    =

0.8281

4)

this is binomial with parameter n=10 and p=0.2

probability =

P(X<=2)=

∑x=0x     (nCx)px(1−p)(n-x)    =

0.6778