5 red, 4 green, and 3 blue marbles. A bag contains 5 red, 4 green, and 3 blue marbles. What is the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting a red marble? StartFraction 1 over 48 EndFraction StartFraction 1 over 12 EndFraction StartFraction 5 over 48 EndFraction StartFraction 5 over 12 EndFraction
The probability of picking a green marble the first time is 3/20 and the probability of picking a yellow marble the second time is 8/20. probabilities are heavily related to percents so it would make sense that the probability of picking a color would be the number of that color divided by the total number.
note that it is really important that the problem said that the marble was replaced. If the marble was not replaced, the probability of picking a yellow marble the second time would be 8/19 if the first marble picked was not a yellow one.
1. Count all of the total probabilities, make it the denominator of your fraction under your favorable possibilities. In this case, you favorable possibility would be the marble you select, so lets start with the blue marble. But, we would repeat this with the other color later. Now, we have 2/10, or 1/5.
2. After you set up your proportion, do the same for the next marble color. The only difference this time is that because you did not replace that one marble you might've picked up before, your denominator would be nine, subtracting that one marble from your total possibilities. Now you would put your total green marbles over your total possibilities. You should get 5/9.
3. Now, set up both the proportions so you multiply them together, 1/5 x 5/9.
4. Your number now should be 5/45, but we will simplify it to get our final answer of 1/9.
A bag contains 10 red marbles and 5 blue marbles (15 marbles in total). You randomly select 3 marbles from the bag.
a) You replace each marble before selecting the next one.
The probability of selecting one blue marble is
then the probability that all 3 marbles are blue is
b) You do not replace each marble before selecting the next one. Each time the number of blue marbles decreases by 1 and the total number of marbles decreases by 1 too. So the probability that all 3 marbles are blue is
1. Count all of the total probabilities, make it the denominator of your fraction under your favorable possibilities. In this case, you favorable possibility would be the marble you select, so lets start with the blue marble. But, we would repeat this with the other color later. Now, we have 2/10, or 1/5.
2. After you set up your proportion, do the same for the next marble color. The only difference this time is that because you did not replace that one marble you might've picked up before, your denominator would be nine, subtracting that one marble from your total possibilities. Now you would put your total green marbles over your total possibilities. You should get 5/9.
3. Now, set up both the proportions so you multiply them together, 1/5 x 5/9.
4. Your number now should be 5/45, but we will simplify it to get our final answer of 1/9.
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