A jar contains four marbles, each a different color: red,

blue, green, and yellow. If you draw two marbles from
the jar, one after another, replacing the first before
drawing the second, what is the probability of getting
a. two red marbles?
b. a red marble on the first draw and a green marble on
the second draw?
c. at least one red marble and one green marble?
d. no yellow marbles?

a) prob (red,red) = (1/4)(1/4) = 1/16

b) prob(red then green) = (1/4)(1/4) = 1/16
c) could be RG or GR
so prob = 1/16 + 1/16 = 1/8
(I don't see where the "at least" comes in, you are only drawing 2 and you want a red AND a green)

d) prob (no yellow, no yellow = (3/4)(3/4) = 9/16

To find the probability of different outcomes, we need to determine the total number of possible outcomes and the number of favorable outcomes.

a. Probability of getting two red marbles:
To calculate this, we need to find the probability of drawing a red marble on the first draw and then another red marble on the second draw with replacement.
Total number of outcomes = 4 marbles (red, blue, green, yellow)
Number of favorable outcomes = 1 red marble on the first draw * 1 red marble on the second draw = 1
Probability = Number of favorable outcomes / Total number of outcomes = 1 / 4 = 0.25 or 25%

b. Probability of getting a red marble on the first draw and a green marble on the second draw:
For this, we also consider replacement, which means we put back the first marble before drawing the second.
Total number of outcomes = 4 marbles (red, blue, green, yellow)
Number of favorable outcomes = 1 red marble on the first draw * 1 green marble on the second draw = 1
Probability = Number of favorable outcomes / Total number of outcomes = 1 / 4 = 0.25 or 25%

c. Probability of getting at least one red marble and one green marble:
We can calculate this by finding the probability of getting one red and one green marble and adding it to the probability of getting two red marbles (as calculated in part a).
Total number of outcomes = 4 marbles (red, blue, green, yellow)
Number of favorable outcomes:
For one red and one green marble:
* Number of favorable outcomes = 1 red marble on the first draw * 1 green marble on the second draw = 1
* Number of favorable outcomes = 1 green marble on the first draw * 1 red marble on the second draw = 1
For two red marbles:
* Number of favorable outcomes = 1 red marble on the first draw * 1 red marble on the second draw = 1
* (Note: We already calculated this in part a.)
Total number of favorable outcomes = 1 + 1 + 1 = 3 (since we are adding the results from the two cases)
Probability = Number of favorable outcomes / Total number of outcomes = 3 / 4 = 0.75 or 75%

d. Probability of getting no yellow marbles:
To calculate this, we need to find the probability of getting either red, blue, or green marbles on both draws.
Total number of outcomes = 4 marbles (red, blue, green, yellow)
Number of favorable outcomes = 3 marbles (red, blue, green) on the first draw * 3 marbles (red, blue, green) on the second draw = 3 * 3 = 9
Probability = Number of favorable outcomes / Total number of outcomes = 9 / 4 = 2.25 or 225%

Note: The probability should always be between 0 and 1. The probability given in part d is incorrect. It should not exceed 1.