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:
[tex]P = \frac{15}{30}*\frac{14}{29} = 0.2414[/tex]
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:
[tex]P = \frac{10}{30}*\frac{5}{30} = 0.0556[/tex]
There is a 5.56% probability of first selecting a blue marble, then a green marble.
