Jar A has 2 red marbles, 4 green marbles, and 3 blue marbles. Jar B has 4 pink marbles, 6 purple marbles, and 2 white marbles. Marcy randomly choo
ses 2 marbles from Jar A, then 2 marbles from Jar B, without replacement in each case. What is the probability that she gets 1 purple marble, 1 pink marble, and 2 green marbles?
A has 9 marbles to start, and B has 12.
P(A=green,green) = 4/9 * 3/8
P(B=purple,pink) = 6/12 * 4/11
P(B=pink,purple) = 4/12 * 6/11
so, add 'em up, since they are independent events
To calculate the probability, we need to determine the total number of possible outcomes and the number of outcomes that satisfy the given conditions.
Step 1: Determine the total number of possible outcomes
In Jar A, Marcy chooses 2 marbles without replacement. There are 2 red + 4 green + 3 blue = 9 marbles in total, so the total number of ways she can choose 2 marbles from Jar A is C(9, 2) = 36.
Similarly, there are C(12, 2) = 66 ways she can choose 2 marbles from Jar B.
The total number of possible outcomes is the product of these two values: 36 * 66 = 2376.
Step 2: Determine the number of outcomes that satisfy the given conditions
Marcy needs to get 1 purple marble, 1 pink marble, and 2 green marbles.
For the purple marble, there are 6 choices from Jar B.
For the pink marble, there are 4 choices from Jar B.
For the green marbles, there are 4 choices from Jar A.
The number of outcomes that satisfy the given conditions is the product of these values: 6 * 4 * C(4, 2) = 144.
Step 3: Calculate the probability
The probability is the number of outcomes that satisfy the conditions divided by the total number of possible outcomes:
Probability = Number of desired outcomes / Total number of possible outcomes
Probability = 144 / 2376
Simplifying this fraction, we get:
Probability = 1 / 11
So the probability that Marcy gets 1 purple marble, 1 pink marble, and 2 green marbles is 1 in 11.
To find the probability of getting 1 purple marble, 1 pink marble, and 2 green marbles, we need to calculate the probability of these events happening in order.
Step 1: Calculate the probability of drawing a purple marble from Jar B.
The probability of drawing a purple marble from Jar B on the first draw is 6/12.
After removing one purple marble, the probability of drawing a second purple marble from Jar B is 5/11.
Step 2: Calculate the probability of drawing a pink marble from Jar B.
The probability of drawing a pink marble from Jar B on the first draw is 4/12.
After removing one pink marble, the probability of drawing a second pink marble from Jar B is 3/11.
Step 3: Calculate the probability of drawing 2 green marbles from Jar A.
The probability of drawing a green marble from Jar A on the first draw is 4/9.
After removing one green marble, the probability of drawing a second green marble from Jar A is 3/8.
Step 4: Calculate the overall probability of getting 1 purple marble, 1 pink marble, and 2 green marbles.
The overall probability is the product of the probabilities from each step:
(6/12) * (5/11) * (4/12) * (3/11) * (4/9) * (3/8) = 0.0364 (rounded to four decimal places).
Therefore, the probability of getting 1 purple marble, 1 pink marble, and 2 green marbles is approximately 0.0364, or 3.64%.