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) |

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