You have 4 red marbles,5 green,7 blue. What is the probability of selecting a red marble, replacing it, and selecting a blue.What is the probability of selecting a red marble, notreplacing it, and selecting a blue. I think 1 is 1/16 and two is 4/32
1st ... 1/4 * 7/16
2nd ... 1/4 * 7/15
is that what the correct answers are?
To calculate the probability of selecting a red marble, replacing it, and then selecting a blue marble, you need to find the product of the probabilities of each individual event.
1. Probability of selecting a red marble: There are 4 red marbles out of a total of 4 + 5 + 7 = 16 marbles. Therefore, the probability of selecting a red marble is 4/16.
2. Probability of selecting a blue marble: There are 7 blue marbles out of a total of 16 marbles. Thus, the probability of selecting a blue marble is 7/16.
Since the marbles are replaced after each selection, the events are independent of each other. To find the probability of two independent events occurring, you multiply the probabilities together:
Probability of selecting a red marble, replacing it, and selecting a blue marble = (4/16) * (7/16) = 28/256 = 7/64.
Therefore, the probability of selecting a red marble, replacing it, and selecting a blue marble is 7/64.
Now, to calculate the probability of selecting a red marble, not replacing it, and then selecting a blue marble:
1. Probability of selecting a red marble: As mentioned above, the probability of selecting a red marble is 4/16.
2. Probability of selecting a blue marble: Once a red marble is not replaced, there are now 15 marbles left, out of which 7 are blue. Therefore, the probability of selecting a blue marble is 7/15.
Again, since the marbles are not replaced, the events are dependent on each other. To find the probability of two dependent events occurring, you multiply the probabilities together:
Probability of selecting a red marble, not replacing it, and selecting a blue marble = (4/16) * (7/15) = 28/240 = 7/60.
Hence, the probability of selecting a red marble, not replacing it, and selecting a blue marble is 7/60.