Answer:
a) There is a 24.14% probability that both marbles are red.
b) There is a 5.56% probability of first selecting a blue marble, then a green marble.
Step-by-step explanation:
a) Two marbles are selected with replacement. Find the probability that both marbles are red.
Initially, there are 30 marbles, of which 15 are red. So there is a 15/30 probability that the first marble selected is red.
After a red marble is selected, there are 29 marbles, of which 14 are red. So there is a 14/29 probability that the second marble selected is red.
The probability that both marbles are red is:
![P = \frac{15}{30}*\frac{14}{29} = 0.2414](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B15%7D%7B30%7D%2A%5Cfrac%7B14%7D%7B29%7D%20%3D%200.2414)
There is a 24.14% probability that both marbles are red.
b) Two marbles are selected without replacement. Find the probability of first selecting a blue marble, then a green marble
There are 30 marbles, of which 10 are blue and 5 are green.
So, there is a 10/30 probability of selecting a blue marble and a 5/30 probability of selecting a red marble.
The probability of selecting a blue marble and then a green marble is:
![P = \frac{10}{30}*\frac{5}{30} = 0.0556](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B10%7D%7B30%7D%2A%5Cfrac%7B5%7D%7B30%7D%20%3D%200.0556)
There is a 5.56% probability of first selecting a blue marble, then a green marble.