Question

Probabilities of pulling 7 Cokes from a cooler with 11 sodas.

a) What is the probability of pulling exactly 7 Cokes from the cooler?

b) What is the probability of pulling more than 7 Cokes from the cooler?

c) What is the probability of pulling at MOST 7 Cokes from the cooler?

Assume it is a .5 chance of pulling a Coke from the cooler.

Answer 1

here this is binomial with parameter n=11 and p=0.5

a)

P(X=7)=

(11C7)0.57(1−0.5)(11-7)    =

0.1611

if using ti-84 press -2nd -vars :binompdf(11,0.5,7)

if using excel use command :binomdist(7,11,0.5,false)

b)

probability of pulling more than 7 Cokes from the cooler :

P(X>7)=1-P(X<=7)=

1-∑x=07 (nCx)px(q)(n-x) =

0.1133

if using ti-84 press 2nd -vars- command :1-binomcdf(11,0.5,7)

if using excel use command :1-binomdist(7,11,0.5,true)

c)

probability of pulling at MOST 7 Cokes from the cooler =P(X<=7) =1-P(X>7)=1-0.1133 =0.8867