Question

26. Towinatadicegame,theplayermustroletwodiceandgeta7or11sum. Thisgamehasa22.2%chanceof winning. Supposeaplayerrollsthedice18times.

a) Whatistheprobabilitythattheywinexactlyonce?
b) Whatistheprobabilitythattheywintwotimesorless?
c) Whatistheprobabilitythattheydonotwinatall?(Thismeansshewinszerotimes.)
d) Whatistheprobabilitythattheywinthreetimesorless?
e) Whatistheprobabilitythattheywinfourormoretimes? (Subtractyouranswerin(d)fromone.) f) Whatistheprobabilitythattheywinfourtimesorless?
g) Whatistheprobabilitythattheywinfiveormoretimes? (Subtractyouranswerin(f)fromone.)

Answer 1

here this is binomial with parameter n=18 and p=0.222

a)

P(X=1)=

(18C1)0.2221(1−0.222)(18-1)    =

0.0560

b)

P(X=2)=

(18C2)0.2222(1−0.222)(18-2)    =

0.1359

c)

P(X=0)=

(nCx)px(1−p)(n-x)    =

0.0109

d)

P(X=3)=

(nCx)px(1−p)(n-x)    =

0.2067

e)

P(X>=4)=1-P(X<=3)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.5905

f)

P(X<=4)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.6308

g)

P(X>=5)=1-P(X<=4)=

1-∑x=0x-1   (nCx)px(q)(n-x) =1-0.6308 =

0.3692