A cube is painted red on all six sides, then cut into 125 smaller congruent cubes.

A small cube is selected at random and rolled. What is the probability that it has a red side facing up?

Jeff123
Sep 13, 2017

#2**+2 **

Thanks, Chozerr,

It is really good that you had a go AND that you stated your lack of confidence.

It is not a really easy question... I'll give it a go

First, like you said, the big cube is cut into 5*5*5

Starting with the top row and working down, I am going to count how many red sides each little cube has.

Top and bottom rows

3*4+2*12+9 = 12+108+9 = 129 red sides on top row and 129 on the bottom one too

3 | 2 | 2 | 2 | 3 |

2 | 1 | 1 | 1 | 2 |

2 | 1 | 1 | 1 | 2 |

2 | 1 | 1 | 1 | 2 |

3 | 2 | 2 | 2 | 3 |

3 rows in the middle

3*(2*4+1*12) = 60 other red sides

2 | 1 | 1 | 1 | 2 |

1 | 0 | 0 | 0 | 1 |

1 | 0 | 0 | 0 | 1 |

1 | 0 | 0 | 0 | 1 |

2 | 1 | 1 | 1 | 2 |

Total number of red sides = 129+129+60 = 318 red sides altogether

There are 125 little cubes so these have a total of 125*6 = 750 sides

So if you choose a little cube at random and roll it I think the probability of rolling a red is 318/750 = 53/125

I think this is correct but there might have been an easier way to do it. I am really not sure. :)

Melody
Sep 13, 2017

#1**+2 **

I'll start by saying that I am unsure whether my answer is correct.

You have a cube which is separated into 125 smaller cubes. This must mean that your cube is 5 smaller cubes long on each side.

This means that the amount of colored small cube sides is 150 (calculated by doing 5*5*6)

A number of sides in total is 750 (125*6)

This would mean that the percentage of colored sides is 20%

So the probability is 1:5 or 20%.

Feel free to correct me if I'm wrong. :)

ChoZerr
Sep 13, 2017

#2**+2 **

Best Answer

Thanks, Chozerr,

It is really good that you had a go AND that you stated your lack of confidence.

It is not a really easy question... I'll give it a go

First, like you said, the big cube is cut into 5*5*5

Starting with the top row and working down, I am going to count how many red sides each little cube has.

Top and bottom rows

3*4+2*12+9 = 12+108+9 = 129 red sides on top row and 129 on the bottom one too

3 | 2 | 2 | 2 | 3 |

2 | 1 | 1 | 1 | 2 |

2 | 1 | 1 | 1 | 2 |

2 | 1 | 1 | 1 | 2 |

3 | 2 | 2 | 2 | 3 |

3 rows in the middle

3*(2*4+1*12) = 60 other red sides

2 | 1 | 1 | 1 | 2 |

1 | 0 | 0 | 0 | 1 |

1 | 0 | 0 | 0 | 1 |

1 | 0 | 0 | 0 | 1 |

2 | 1 | 1 | 1 | 2 |

Total number of red sides = 129+129+60 = 318 red sides altogether

There are 125 little cubes so these have a total of 125*6 = 750 sides

So if you choose a little cube at random and roll it I think the probability of rolling a red is 318/750 = 53/125

I think this is correct but there might have been an easier way to do it. I am really not sure. :)

Melody
Sep 13, 2017