A bag contains 6 red marbles, 6 blue marbles, 10 white marbles and 7 yellow marbles. You are asked to draw 4 marbles from the bag without replacement. In how many ways can you draw two blue marbles? what formula do you use for questions like these

Guest Nov 8, 2015

#1**+5 **

A bag contains 6 red marbles, 6 blue marbles, 10 white marbles and 7 yellow marbles. You are asked to draw 4 marbles from the bag without replacement. In how many ways can you draw two blue marbles? what formula do you use for questions like these

I am going to play with this question a little

If ALL the b***s are different. I mean, you have blue 1 blue 2 etc then

Number of ways of choosing 2 blue from 6 is 6C2 = 15

Number of ways of choosing 2 from the others 23C2 = 253

Total = 15*253 = 3795 ways

The number of ways that 4 marbles can be drawn with no restrictions is 29C4 = 23751

So the probablility of drawing 2 blue is 3795 / 23751 = 0.1598 (4 dp)

This is the way it must be done if you are looking at probablilities

**BUT you are not concerned with probablilities and I think below is what the question may really be asking.**

Lets see,

6 red marbles, 6 blue marbles, 10 white marbles and 7 yellow marbles

you could have

Blue | White | Red | Yellow | THE 4 B***S |

BB | WW | BBWW | ||

BB | W | R | BBWR | |

BB | W | Y | BBWY | |

BB | RR | BBRR | ||

BB | R | Y | BBRY | |

BB | YY | BBYY | ||

6 WAYS |

So there are 6 different combinations that could include 2 blue b***s BUT they are NOT all equally likely to be drawn.

Melody
Nov 8, 2015

#1**+5 **

Best Answer

A bag contains 6 red marbles, 6 blue marbles, 10 white marbles and 7 yellow marbles. You are asked to draw 4 marbles from the bag without replacement. In how many ways can you draw two blue marbles? what formula do you use for questions like these

I am going to play with this question a little

If ALL the b***s are different. I mean, you have blue 1 blue 2 etc then

Number of ways of choosing 2 blue from 6 is 6C2 = 15

Number of ways of choosing 2 from the others 23C2 = 253

Total = 15*253 = 3795 ways

The number of ways that 4 marbles can be drawn with no restrictions is 29C4 = 23751

So the probablility of drawing 2 blue is 3795 / 23751 = 0.1598 (4 dp)

This is the way it must be done if you are looking at probablilities

**BUT you are not concerned with probablilities and I think below is what the question may really be asking.**

Lets see,

6 red marbles, 6 blue marbles, 10 white marbles and 7 yellow marbles

you could have

Blue | White | Red | Yellow | THE 4 B***S |

BB | WW | BBWW | ||

BB | W | R | BBWR | |

BB | W | Y | BBWY | |

BB | RR | BBRR | ||

BB | R | Y | BBRY | |

BB | YY | BBYY | ||

6 WAYS |

So there are 6 different combinations that could include 2 blue b***s BUT they are NOT all equally likely to be drawn.

Melody
Nov 8, 2015