Question

1. Suppose that the likelihood that someone who logs onto a particular ‘shopping mall’ website will purchase an item is .33. If the site has 7 people accessing it in the next minute, what is the probability that:
   a) none of the individuals will purchase an item?
   b) exactly three individuals will purchase an item?
   c) at least three individuals will purchase an item?
   d) at most three individuals will purchase an item?
   

Answer 1

here this is binomial with parameter n=7 and p=0.33

a)

probability =

P(X=0)=

(nCx)px(1−p)(n-x)    =

(1-0.33)7 =

0.0606

b)

probability =

P(X=3)=

(10C3)0.333(1−0.33)(10-3)    =

0.2535

c)

probability =

P(X>=3)=

1-P(X<=2)=

1-∑x=02 (10Cx)0.33x(1−0.67)(10-x)    =

0.4217

d)

probability =

P(X<=3)=

∑x=03 (10Cx)0.33x(1−0.67)(10-x)    =

0.8318