Question

You and a friend are rolling a set of 7 dice. The game works such that if a die shows the values 1, 2, 3, or 4 you will get a point for that die. Each die that shows 5 or 6 your friend will get a point for.
Construct a probability model for a single roll of the dice then answer the following.

A)What is the probability you made 2 points?

B)What is the probability that your friend will score 2 points?

C)What is the probability you score 4 or more points in this round?

D)If we play a second round of this game, what is the probability that you will have exactly 6 points at the end of the second round?

E)If we play another round what is the probability you will have 10 or more points?

Please show step by step.

Answer 1

X = number of points made by me

X follow binomial distribution

n = 7, p = 2/3

a) P(X = 2) = 7C2 * (2/3)^2* (1/2)^5

= 0.0384

b)

friend score 2 point means we score 7-2 = 5 points

P(X = 5) = 0.3072

c)

P(X >= 4)

= 0.8267

d)

now n = 14

P(X = 6) = 0.0402

e)

now n = 21

P(X >= 10)

= 0.9788

	n	p	x
a)	7	0.666667	2	0.038409
b)	7	0.666667	5	0.30727
c)	7	0.666667	4	0.826703
d)	14	0.666667	6	0.040183
e)	21	0.666667	10	0.978806

formulas

	n	p	x
a)	7	=2/3	2	=BINOM.DIST.RANGE(B2,C2,D2,D2)
b)	7	=2/3	5	=BINOM.DIST.RANGE(B3,C3,D3,D3)
c)	7	=2/3	4	=BINOM.DIST.RANGE(B4,C4,D4,B4)
d)	14	=2/3	6	=BINOM.DIST.RANGE(B5,C5,D5,D5)
e)	21	=2/3	10	=BINOM.DIST.RANGE(B6,C6,D6,B6)