A bag contains 3 red marbles, 3 blue marbles and 3 yellow marbles. Which of the following methods of selecting 2 marbles will have the greater probability of choosing 2 red marbles?

Randomly choose a marble don't replace it
then randomly choose another marble

and the other method is ... ?

A promissory note for $15,000 was written on March 10( for 180 days at 6%. It

was discounted on June 15 at 12.5%.
Find a) the maturity value b) Maturity date c) term of the discount d) discount
amount e) The proceeds.

To determine which method of selecting 2 marbles will have the greater probability of choosing 2 red marbles, let's consider both scenarios:

Method 1: Randomly choose a marble without replacing it and then randomly choose another marble.
In this method, we need to calculate the probability of selecting 2 red marbles.

Step 1: Calculate the probability of selecting the first red marble:
There are 3 red marbles out of 9 total marbles. So, the probability of selecting a red marble on the first draw is 3/9.

Step 2: Calculate the probability of selecting a second red marble:
Once the first marble has been selected, there are now only 8 marbles left in the bag. Since we do not replace the first marble, there are now only 2 red marbles remaining out of the 8 marbles. Therefore, the probability of selecting a red marble on the second draw is 2/8.

Step 3: Calculate the probability of selecting 2 red marbles:
To find the probability of both events occurring (selecting a red marble on the first draw and a red marble on the second draw), we multiply the probabilities from Step 1 and Step 2 together: (3/9) * (2/8) = 6/72 = 1/12.

Method 2: Randomly choose a marble, replace it, and then randomly choose another marble.
In this method, we also need to calculate the probability of selecting 2 red marbles.

Step 1: Calculate the probability of selecting a red marble on the first draw:
Using the same reasoning as before, the probability of selecting a red marble on the first draw is still 3/9.

Step 2: Calculate the probability of selecting a red marble on the second draw:
Since we replace the first marble back into the bag, the total number of marbles remains the same at 9. The probability of selecting a red marble on the second draw is still 3/9.

Step 3: Calculate the probability of selecting 2 red marbles:
Again, we multiply the probabilities from Step 1 and Step 2 together: (3/9) * (3/9) = 9/81 = 1/9.

Comparing the two methods, we can see that Method 1 (randomly choosing a marble without replacing it) has a greater probability of choosing 2 red marbles with a probability of 1/12, while Method 2 (randomly choosing a marble, replacing it, and then randomly choosing another marble) has a probability of 1/9. Therefore, Method 1 has the greater probability of selecting 2 red marbles.