there are 4 red marbles 7 blue and 5 green
what is the probability of picking a red replacing it and then getting a blue
what is the probability of picking a red this time setting it aside and getting a blue
why or why not are the answers the same
I have been stuck for a while please help I want to know the way to solve this considering I have mcas soon
In the first case, since you are returning the marble, the two events are independent, that is,
whatever happened in the first pick has no effect on the second pick
so prob(your event) = (7/16)(7/16) = ....
In the 2nd case you are not returning the marble, so for the second pick there would only be 1 5 marbles left
so .....
let me know what your answer is
1. because it would be 4/16 for red and 7/16 for blue I don't know how to make them both into a single probability
2.then there is 4/16 red and 7/15 blue but again I have no clue on how to make them into one
You just multiply them.
#1 prob = (4/16)(7/16) = 7/184 or appr .038
#2 prob = (4/16)(6/15) = ...
7/60 i think would be the answer for 2
and how did you get 184
To calculate the probability of picking a red marble, replacing it, and then getting a blue marble, we need to consider the total number of marbles and the number of desired outcomes.
1. Probability of picking a red, replacing it, and then getting a blue:
The probability of picking a red marble is 4 out of the total 16 marbles (4 red + 7 blue + 5 green). After picking a red marble, the number of blue marbles remains the same, so the probability of picking a blue marble is 7 out of 16. Since you are replacing the marbles after each pick, the events are independent. Therefore, the probability of both events occurring is the product of their individual probabilities:
P(Red and Blue) = P(Red) * P(Blue | Red)
= (4/16) * (7/16)
= 28/256
= 7/64
2. Probability of picking a red and setting it aside, and then getting a blue:
The probability of picking a red marble and setting it aside is 4 out of the total 16 marbles. After setting the red marble aside, the total number of marbles decreases to 15, but the number of blue marbles remains the same. Therefore, the probability of picking a blue marble is 7 out of 15. Again, since the events are independent, we multiply the probabilities:
P(Red and Blue) = P(Red) * P(Blue)
= (4/16) * (7/15)
= 28/240
= 7/60
The answers are different because the probability calculations are affected by the number of marbles available for selection. In the first scenario, the total number of marbles remains the same after each pick because we replace the marble. However, in the second scenario, the total number of marbles decreases by 1 after the first pick, affecting the probability calculation. Thus, the probabilities of picking a blue marble in each scenario are different.
When solving probability problems, it is crucial to consider whether replacement or withholding affects the calculations. Understanding independence of events and adjusting the calculations accordingly will help you arrive at the correct answers. Good luck with your MCAS! If you have any additional questions, feel free to ask.