Question

In the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 29 times, find the probability of the following events.

A. The ball falls into the green slots 4 or more times.

Probability =

B. The ball does not fall into any green slots.

Probability =

C. The ball falls into black slots 10 or more times.

Probability =

D. The ball falls into red slots 9 or fewer times.

Probability =

Answer 1

red=18

black=18

green=2

total=38

p(red)=18/38 =0.4737

p(black)=18/38=0.4737

p(green)=2/38=0.0526

1) nCx p^x q^n-x

nCx=29C4=23751

p^x= 0.0526^4 =0.00000765496

q^n-x=q^29-4=q^25=(1-p)^25=0.944^25=0.23675538044

=23751*0.00000765496*0.23675538044

=0.043017

2) 1-(nCx p^x q^n-x)

=1-(29*0.0526*(1-0.0526)^28)

=1-(29*0.0526*0.22025)

=1-0.3359

=0.6640

3)nCx p^x q^n-x

nCx=29C10=2003001

p^x= 0.4737^10 =0.0005688

q^n-x=q^29-10=q^19=(1-p)^19=0.00000505

=2003001*0.0005688*0.00000505

=0.0057

4)

nCx p^x q^n-x

nCx=29C9=10015005

p^x= 0.4737^9 =0.00120

q^n-x=q^29-10=q^20=(1-p)^20=0.00000265

=10015005*0.00120*0.00000265

=0.0318

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