A bag contains 4 white, 3 blue, and 5 red marbles. find the probability of choosing 3 blue marbles in a row if the marbles are replaced

Question

A bag contains 4 white, 3 blue, and 5 red marbles.  find the probability of choosing 3 blue marbles in a row if the marbles are replaced

goldphenoix · Answer

Well. There's 12 possible outcomes. What is a chance of you getting a blue?
There's a 3/12 chance of getting a blue because there's 3 blue out of the 12 total outcome.
But what is the probability of getting 3 blue marbles in a row?
Well, the probability of getting a blue marble is a 3/12. The probability of getting another blue marble is 3/12 x 3/12. The probability of getting another blue marble is 3/12 x 3/12 x 3/12. Why? Well, the marbes are being replaces. So the chance of getting the same outcome is a same. Except you do 3/12 x 3/12 x 3/12 because that's the probability of getting 3 blue marbles in a row. So: $$\large \large \frac{ 3 }{ 12 } \times \frac{ 3 }{ 12 } \times \frac{ 3 }{ 12 } = \frac{ 27 }{ 1728 }$$ 27/1728 can be simplify to 1/64. So the probability of getting 3 blue marbles in a row is 1/64.
I hope this help!

anonymous · Answer

there are to more question  I have can you help please:)?

goldphenoix · Answer

Sure. :)

anonymous · Answer

find the probability of choosing a blue marble,then a red marble if the marbles aren't replaced

anonymous · Answer

find the probability of choosing 2 white marbles in a row if the marbles are not replaced

goldphenoix · Answer

The probability of choosing a blue marble is 3/12. (Remember?) Now what is the probability of getting a red marble? It's 5/11 because there's 5 red out of the new total outcome. What you want to od is 3/12 x 5/11. $$\large \large \frac{ 3 }{ 12 } \times \frac{ 5 }{ 11 } = \frac{ 15 }{ 132 } = \frac{ 5 }{ 44}$$ So the probability of choosing a blue marble and then a red marble without replacing is 5/44.

goldphenoix · Answer

The probability of choosing a white marble is 4/12. What is the probability of choosing another whtie marble, without replacing. Well, it would be 3/11. Why? Well there's a chance of getting a white marble (4/12), and if you got a white marble, the next chance of getting a white marble is 3/11, because the the total outcome has decreased by 1, and so does the total whtie marble. So 4/12 x 3/11 is equal to 12/132. 12/132 can be simplify to 1/11.
 I hope this help. :)

anonymous · Answer

Thank you @GoldPhenoix you are the best!:D

anonymous · Answer

WOW i had these EXACT same questions and this help SO MUCH! Thanks to u both!