a bag of 100 marbles contains 30 blue, 25 green, 25 mixed,and 20 clear. what is the probality of selecting a blue?
ablue and green? a marble that is not clear? ablue on the first draw and a clearon the second draw? a
prob (of selecting a blue) = 30/100 = 3/10
if you are picking one marble,
prob(blue AND green) = 0
if you are picking 2 then it could be
BG or GB
which is (3/10)(25/99) + (25/100)(30/99) =5/33
prob(not a clear) = 80/100 = 4/5
prob(blue, then a clear) = (30/100)(20/99) = 2/33
To find the probabilities for each scenario, we need to know the total number of marbles and the number of marbles in each category. From the given information, we have:
Total number of marbles: 100
Number of blue marbles: 30
Number of green marbles: 25
Number of mixed marbles: 25
Number of clear marbles: 20
1. Probability of selecting a blue marble:
The probability of selecting a blue marble is the number of blue marbles divided by the total number of marbles: 30/100 = 0.3 or 30%.
2. Probability of selecting a blue and green marble:
To find the probability of selecting a blue and then a green marble, we multiply the probability of selecting a blue marble by the probability of selecting a green marble. Since the marbles are drawn without replacement (meaning the first marble is not put back into the bag before the second draw), the probability changes for each selection.
- Probability of selecting a blue marble: 30/100 = 0.3 or 30%
- Probability of selecting a green marble after selecting a blue marble: 25/99 (since there are now 99 marbles in the bag, with one blue marble already drawn)
So, the probability of selecting a blue marble and then a green marble is (30/100) * (25/99) = 0.076 or 7.6%.
3. Probability of selecting a non-clear marble:
To find the probability of selecting a marble that is not clear (any color other than clear), we need to sum up the number of marbles in each category except clear and then divide it by the total number of marbles.
- Number of non-clear marbles: 30 + 25 + 25 = 80
- Probability of selecting a non-clear marble: 80/100 = 0.8 or 80%
4. Probability of selecting a blue marble on the first draw and a clear marble on the second draw:
To find the probability of selecting a blue marble on the first draw and a clear marble on the second draw, we multiply the probabilities of each draw. Since the marbles are drawn without replacement, the probability changes for each selection.
- Probability of selecting a blue marble on the first draw: 30/100 = 0.3 or 30%
- Probability of selecting a clear marble on the second draw after the blue marble has been removed: 20/99 (since there are now 99 marbles in the bag, with one blue marble already drawn)
So, the probability of selecting a blue marble on the first draw and a clear marble on the second draw is (30/100) * (20/99) = 0.0606 or 6.06%.
To calculate the probabilities, we need to know the total number of marbles in the bag. In this case, the bag contains 100 marbles.
1) To calculate the probability of selecting a blue marble, we divide the number of blue marbles (30) by the total number of marbles (100):
Probability of selecting a blue = 30/100 = 0.3 or 30%
2) To calculate the probability of selecting a blue and green marble, we add the number of blue marbles (30) and green marbles (25) and divide it by the total number of marbles (100):
Probability of selecting blue and green = (30 + 25)/100 = 55/100 = 0.55 or 55%
3) To calculate the probability of selecting a marble that is not clear, we need to subtract the number of clear marbles (20) from the total number of marbles (100) and then divide it by the total number of marbles (100):
Probability of selecting a marble that is not clear = (100 - 20)/100 = 80/100 = 0.8 or 80%
4) To find the probability of selecting a blue marble on the first draw and a clear marble on the second draw, we calculate the probability of each event independently and then multiply the probabilities together. On the first draw, the probability of selecting a blue marble is 30/100. Assuming the marble is not replaced, there would be 99 marbles left in the bag, including 20 clear marbles. So, on the second draw, the probability of selecting a clear marble would be 20/99. To find the joint probability, we multiply the probabilities together:
Probability of blue on the first draw and clear on the second draw = (30/100) * (20/99) = 600/9900 = 0.0606 or approximately 6.1%