Question

A box contains 30 marbles: 15 red, 10 blue, and 5 green. a) Two marbles are selected with replacement. Find the 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

Answer 1

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:

$P = \frac{15}{30}*\frac{14}{29} = 0.2414$

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:

$P = \frac{10}{30}*\frac{5}{30} = 0.0556$

There is a 5.56% probability of first selecting a blue marble, then a green marble.