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.

Math   Statistics-And-Probability   
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Homework Answers

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)
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