I have a probability question, I need to know how you get the answer not just the answer. Question below.?

Question

A bag contains 15 marbles, of which 8 are red, 5 are blue, and 2 are white. Two marbles are drawn randomly from the bag one after the other, without replacement. What is the probability that both marbles are red?

Answer 1

15 is our "total". Right?
8 of those 15 are "red". You randomly select one of the 15, and there is an 8/15 chance that you will select red, 5/15 chance that you will select blue, and 2/15 chance that you will choose white. Add them all up and they add to 1. This is to double-check that we are working with all of the possibilities.

Key words, "without replacement". Once you've chosen the first marble, there are 14 left. We assume that you chose red the first time, since if you didn't, then this second case would never occur. the number of red marbles changes to 7, the total marbles changes to 14. the other numbers remain the same. NOW the chance of choosing a red marble becomes 7/14.

multiply these two numbers together to obtain the probability that both events occur.
(8/15) * (7/14) = ?

Answer 2

You need to multiply the probability of both events.

The probability of the first event is 8/15 because you have 8 red marbles in a bag of 15. Now since your question said "without replacement" you now have 14 marbles in the bag. We have to assume the first marble is red so the probability of the second event is 7/14 because you now have 7 red marbles in a bag of only 14.

Now multiply the probability of both events 8/15 * 7/14 and you get .267 or a 27% chance of pulling two red marbles.

Now if your question said with replacement, you would have 8/15 * 8/15 because you would put the red marble back and have just as good a chance at drawing a red one again as you did in drawing the first marble. That would be a .284 or 28% chance of pulling two red marbles.

Hope this helps...Good Luck with your Math.

Answer 3

This is a conditional probability, where one depends on the other occuring.

Therefore, you must multiply the two probabilities of each event occurring to get the probability that both occur.

The first event, drawing a red marble from the bag, has an 8 in 15 chance of occurring since there are 8 red marbles and 15 total marbles.

The second event, drawing a second red marble (WITHOUT REPLACEMENT), occurs only if the first one takes place. That means there must be 7 red marbles left and 14 total marbles. The probability of drawing a second red marble IF the first event occurs is 7/14.

Now, to get the probability that both events occur, namely that two red marbles will be drawn consecutively from the bag, without replacement, you multiply the two probabilities.

(8/15) * (7/14) = 56 / 210

Taking common denominators out, 56 / 210 = 4 / 15

Therefore, there is a 4 / 15 probability that you will draw two consecutive red marbles from the bag, without replacement.

Answer 4

Let's consider that you get first one marble and then the other. As there's no replacement (meaning that you put not the first marble again in the bag before taking the second one), the entire process happens as follows:

1) INITIALLY: you have a bag with 15 marbles (8 red, 5 blue, 2 white)
2) You draw one marble (that we want to be red)
3) If step 2 was succesful, we now have 14 marbles (7 red, 5 blue, 2 white)
4) Again you draw one marble (that you want red)
5) If step 4 was succesul, you have at the end 13 marbles in the bag (6 red, 5 blue, 2 white)

So, all the problem reduces to answering 3 questions:

Q1- What is the probability of taking a red marble in step 2?
Q2- What is the probability of taking a red marble in step 4?
Q3- What is the probability of taking a red marble in BOTH steps.

Let's answer Q1. This is easy: we have 8 red marbles in a total of 15 marbles. So, the probability of obtaining a red marble in step 2 is: 8/15 (you say usually: "I have 8 chances in 15 of obtaining a red marble")

Q2: Similarly, the probability of drawing a red marble in step 4 is 7/14 (as they are 7 red marbles in a total of 14 marbles) (in usual terms: "I have 7 chances in 14 of obtaining a red marble")

Q3: And the combined probability is the product of both values, e.g. you have first 8 chances of 15 of succeeding, and then 7 chances of 14 of succeding, provided that you already suceeded at the first step. So, the combined value is:

Probability(both marbles are red) = (8/15) * (7/14)

Obseve that 7/14 = 1/2, so:

Probability(2 red marbles) = (8/15)*(1/2) = 4/15

Hope it was clear!

Answer 5

Well 15/100 = 6.66..., so if all the marbles were separate, there would be a rough 6.66% chance for each.

There are 8 reds, so there is a 53.28% chance you'll pick a red.
There are 5 blues so there is a 33.3% chance you'll get a blue,
There are 2 whites leaving 13.32% chance of picking one of them.

So the probability is probably a bit more than half. Sorry that's not too specific but I was trying to work it out quickly. :P Hope it is somewhat useful...

Answer 6

The probability of that is around 8/15

Answer 7

4/15

Answer 8

the probability will be:
the prob that the 1st one is red= 8/15
the prob that the 2nd is red= 7/14
The prob that both are red is the product of 8/15*7/14= 4/15 which is your answer

Answer 9

1st marble you draw is red - probability 8/15

2nd red, given that 1st one was red - probability 7/14

Multiply them, get the answer.

Answer 10

a) which will be fifty 8% of 40 4%. So multiply 40 4 with information from fifty 8/100 to get the share; that may be the answer. (b) i imagine that's 100% - 26%, which may be seventy 4% (c) i imagine that's 26% of 6.5%. with slightly of success my numbers help you? (d) which will be 40 2% of twenty-2%.