There are 6 blue marbles, 9 purple marbles, 4 orange marbles, and 3 green marbles in a bag. If Sally picks two marbles without replacement, what is the probability of getting one orange and one purple marble?
To find the probability of getting one orange and one purple marble, we need to first determine the total number of possible marble combinations when Sally picks two marbles without replacement.
In this case, there are a total of 6 + 9 + 4 + 3 = 22 marbles in the bag.
To calculate the probability, we need to consider two scenarios:
1. Picking an orange marble first and a purple marble second.
2. Picking a purple marble first and an orange marble second.
1. Picking an orange marble first and a purple marble second:
The probability of picking an orange marble first is 4/22 (since there are 4 orange marbles out of 22).
After Sally picks an orange marble, there will be 3 orange marbles left in the bag.
The probability of picking a purple marble second is 9/21 (since there will be 21 marbles left and 9 of them are purple).
2. Picking a purple marble first and an orange marble second:
The probability of picking a purple marble first is 9/22 (since there are 9 purple marbles out of 22).
After Sally picks a purple marble, there will be 8 purple marbles left in the bag.
The probability of picking an orange marble second is 4/21 (since there will be 21 marbles left and 4 of them are orange).
Now, we can calculate the probability of each scenario and add them together to find the probability of getting one orange and one purple marble:
(4/22) * (9/21) + (9/22) * (4/21) = 36/462 + 36/462 = 72/462 = 12/77.
Therefore, the probability of getting one orange and one purple marble is 12/77.
orange = 4/22
then purple = 9/21
4/22 * 9/21 = (2/11)(3/7) = 6/77
or
purple = 9/22
then orange = 4/21
so 6/77 again
add them 12/77