SOLUTION: Suppose an opaque jar contains 4 red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first o

Algebra ->  Permutations -> SOLUTION: Suppose an opaque jar contains 4 red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first o      Log On


   

Question 1042367: Suppose an opaque jar contains 4 red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first one.
What is the probability of getting a green marble and a red marble together? (Enter your probability as a fraction.
Hint: How is this exercise different from finding the probability of getting a green marble first and a red marble second?)
I really need help on this one if anyone is available.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let R%5B1%5D = the event that the first draw is red,
G%5B1%5D = the event that the first draw is green,
R%5B2%5D = the event that the second draw is red,
G%5B2%5D = the event that the second draw is green.
Then P(R%5B1%5D&R%5B2%5D) = %284%2F14%29%2A%283%2F13%29+=+6%2F91,
P(R%5B1%5D&G%5B2%5D) = %284%2F14%29%2A%2810%2F13%29+=+20%2F91,
P(G%5B1%5D&R%5B2%5D) = %2810%2F14%29%2A%284%2F13%29+=+20%2F91, and
P(G%5B1%5D&G%5B2%5D) = %2810%2F14%29%2A%289%2F13%29+=+45%2F91.
What we're interested at are events R%5B1%5D&G%5B2%5D and G%5B1%5D&R%5B2%5D. Since these are mutually exclusive events, the probability is 20%2F91%2B20%2F91+=+highlight%2840%2F91%29.