What is the probability of drawing 2 blue marbles if the first marble is NOT placed back in the bag before the second draw

Question

These marbles are placed in a bag and 2 of them are randomly drawn. What is the probability of drawing 2 blue marbles if the first marble is NOT placed back in the bag before the second draw      2 yellow,3 pink, 5 blue    

Answer 1

Elizabeth,

 

Break it down into two parts. First, what is the probability of drawing a blue marble on the first draw?

Since there are 5 blue marbles and 10 total, the probability is 5⁄10, or 1/2.

 

Now since we no longer have that blue marble, there are 4 blue marbles and 9 total. The chances of drawing a blue marble are 4/9.

 

Therefore, the chance that both marbles drawn are blue is the chance that the first one is blue times the chance that the second one is blue.

 

1/2 * 4/9 = 4/18 = 2/9

 

Remember, math is always trying to trick you. It wants you to try and do the whole big problem at once, which can be difficult. Break it down into smaller problems, then use your answers to small parts to find the answer to the big question.

 

Hope that helps,

 

Danny

Answer 2

First we need to calculate the probability of drawing a blue marble on our first draw.

 

If we have 2 yellow, 3 pink, and 5 blue marbles we have a total of 10 marbles. So we have 10 possible outcomes for our first draw. Next we need to calculate our desired outcome. We want to draw a blue marble and we have 5 of them in the bag so our probability will be our desired outcome / the number of possible outcomes or 5/10. This can be reduced to 1/2.

 

Next we need to calculate the probability of drawing a blue marble with our second draw, however, since the marble is NOT being placed back into the bag our total number of possible outcomes has been reduced to 9. (We started with 10 marbles, pulled one out, and are not putting it back.) We've also reduced the total number of blue marbles by one so instead of having 5 desired outcomes we now only have 4 for a probability of drawing a blue marble on our second draw being 4/9.

 

But we're not done yet, we need to combine these probabilities by multiplying the likelihood of the first event occurring by the second event occurring.

 

1/2 * 4/9 = 4/18 which can be reduced to 2/9.

 

I hope this helps :) Please let me know if you have any questions. Have a wonderful evening!