Question

# You and a friend are rolling a set of 7 dice. The game works such that...

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.

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)

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