Question

to demonstrate probabilities, a mathematics teacher had students draw marbles from a bag which contained 6 yellow marbles and 10 blue marbles. During class, the bag was dropped and 2 yellow marbles and 3 blue marbles were lost. Explain whether the loss of marbles changes the probability of drawing a blue marble from the bag. Be sure to state whether the probability of choosing a blue marble stays the same, increase or decreases once the marbles were lost? Explain why you believe this.

Answer 1

4Okay, so here's how you will do the problem.

first lets find out how many marbles there are in total. At first, there are 16 marbles. (6 yellow + 10 blue)

knowing this
P(Yellow) = 6/16. that simplifies to 3/8
P(Blue) = 10/16. that simplifies to 5/8

We can tell these are correct because when added together the probabilities equal 1 (meaning there's no missing probabilities)

Now, 2 yellow marbles and 3 blue marbles are removed.

this means there are now 4 yellow marbles and 7 blue marbles. this brings the total amount of outcomes is 11.

Now
P(yellow) = 4/11
P(blue = 7/11

we can cross multiply or find out the decimal values and compare to find out if the two are equal

3/8.× 4/11
33........32

5/8 × 7/11
55....56

We will come back to what this shows us in a moment

yellow - .375 (3/8) > .36 repeated
blue - .625 (5/8) < .63 repeated

Both methods show that the probability CHANGED. So, YES the probabilities were affected.

in method one, the cross multiplying show that yellow probability goes down and blue probability goes up. Using the decimals shows the same

hope this helps!