Probability Homework

Question

Suppose a jar contains 12 red marbles and 29 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.

Write your answer in decimal form, rounded to the nearest thousandth.

Answer: 

Answer 1

Hey!

So for this problem, we need to figure out what we're being asked. It really depends on what the question means by reaching into a jar. Is it asking at the same time? Or at two different times? (for this one, I'd suggest thinking back in class to any other similar practice problems)

If we are talking about picking two reds, one at a time:

1. lets figure out how many total number of marbles you have
2. 12 red+ 29 blue = total marbles
3. 41 = total marbles
4. 1st pull: 12 red marbles / 41 total marbles = 0.2926
5. 2nd pull: (we removed 1 red, so its 11 red marbles now and 40 total marbles- we removed one marble) 11 red marbles/ 40 total marbles = 0.275
6. So now, we have to multiply the probability of both: 0.2926 * 0.275 = 0.0804
7. Finally, let's round it to the nearest thousandth: 0.080 (since the ten thousandth number is 4, we round down to 0 and not up to 1)

I'm going to leave this here, if this isn't what is being asked for, I'll also do my best to post the other possible way: if it's two at the same time.

Best of wishes! You got this!

Answer 2

12 red, 29 blue

randomly select 2

what is the probability of both red?

P(1st R)= 12/(12+29) = 12/41

P(2nd R)= 11/40

P(both R) = (12/41)(11/40) = 33/410

= about .0804878

= 0.080 rounded to nearest thousandth = 8% chance

that's the solution for selection Without Replacement, which is how the problem seems to read

if you picked one, put it back and then picked the 2nd

odds are slightly different,that's selection With Replacement

P(2R)= 14241 x 12/41 = 144/41^2 = about .086= about 9%