7. A bag contains 7 green marbles, 9 red marbles, 10 orange marbles, 5 brown marbles, and 10 blue marbles. You choose a marble, replace it, in choose again. What is P(red, then blue)?
A. 77/164
B. 19/41
C. 90/1681
D. 45/41
I absolutely know is is C. 90/1681 but I need someone to help me work through it because I need to show how I got to the answer. Thank You!
you're kidding, right? Why not show your work, so we can see whether you did it right...
41*41 = 1681 ...
To find the probability of choosing a red marble first and then a blue marble, we need to calculate the probability of choosing a red marble and the probability of choosing a blue marble, given that we replaced the first marble back into the bag.
Step 1: Calculate the probability of choosing a red marble.
There are a total of 7 green marbles, 9 red marbles, 10 orange marbles, 5 brown marbles, and 10 blue marbles, making a total of 41 marbles. So, the probability of choosing a red marble is 9/41.
Step 2: Calculate the probability of choosing a blue marble.
Since we replaced the first marble back into the bag, the probabilities of choosing a blue marble each time are independent. Therefore, the probability of choosing a blue marble is 10/41.
Step 3: Calculate the overall probability.
To calculate the probability of both events occurring (choosing a red marble first and then a blue marble), we multiply the probabilities of each event. So, the probability of choosing a red marble, and then a blue marble is (9/41) * (10/41) = 90/1681.
Therefore, the answer is C. 90/1681.