A bag contains the following marbles:6 red,4 orange,3 yellow,2 blue and 5 green. You choose a marble at random and do not replace it. Then you select another marble.
P(red,then blue)3/95
P(orange,then blue) 2/95
P(blue,then yellow) 3/190
P(red,then yellow) 9/190
P(blue,then green) 1/38
P(Red,then red)9/95
P(red, blue) = 6/20 * 2/19 = 12/380 =3/95
P(blue, Yellow) = 2/20 * 3/19 = 6/380 = 3/190
I only checked two, but if you did the same process and your math is correct, they should all be right.
To find the probability of selecting two marbles in a specific order, you need to consider the total number of marbles and the number of marbles of each color in the bag.
For example, let's calculate the probability of selecting a red marble first and then a blue marble:
Step 1: Determine the total number of marbles in the bag.
There are 6 red marbles + 4 orange marbles + 3 yellow marbles + 2 blue marbles + 5 green marbles = 20 marbles in total.
Step 2: Calculate the probability of selecting a red marble first.
There are 6 red marbles in the bag, so the probability of selecting a red marble first is 6/20.
Step 3: After removing one red marble, there are now 19 marbles left in the bag.
Step 4: Calculate the probability of selecting a blue marble.
There are 2 blue marbles remaining in the bag, so the probability of selecting a blue marble second is 2/19.
Step 5: Multiply the probabilities together to get the overall probability.
The probability of selecting a red marble first and then a blue marble is (6/20) * (2/19) = 12/380 = 3/95.
You can follow the same steps to calculate the probabilities of other combinations mentioned in the question.