Question

A bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. What is the probability of choosing a green marble, not replacing it, and then choosing a red marble?

1/16
1/12
1/4
1/2​

Answer 1

StartFraction 1 over 12 EndFraction

Explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

so

Let

x------> size of the event space

y-----> size of the sample space

so

`P=(x)/(y)`

In this problem we have

Part 1) Find the probability of choosing a green marble

we have

`x=1` ---> number of green marbles

`y=1+1+1+1=4` ----> total marbles in the bag

substitute

`P=(1)/(4)`

Part 2) Find the probability of choosing a red marble

we have

`x=1` ---> number of red marbles

`y=3` ----> total marbles in the bag

substitute

`P=\frac{1}3}`

Part 3) Find the probability of choosing a green marble, not replacing it, and then choosing a red marble

Multiply both probabilities

`P=(1)/(4)*(1)/(3)=(1)/(12)`

therefore

StartFraction 1 over 12 EndFraction

Answer 2

`(1)/(12)`

Explanation:

`P(G) =(1)/(4) *P(R)=((1)/(3) )\\((1)/(4) )((1)/(3) ) = (1)/(12)`