Question

An opaque bag contains 5 green marbles, 3 blue marbles, and 2 red marbles. if two consecutive marbles are drawn without replacement what is the probability that the first one will be green and the second one red? ​

a. 0.51
b. 0.10
c. 0.11
d. 0.16

Answer 1

Option c. 0.11

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 that

Two consecutive marbles are drawn without replacement

step 1

Find out the probability that the first one will be green

`x=5`

`y=5+3+2=10`

substitute

`P=(5)/(10)=(1)/(2)`

step 2

Find out the probability that the second one will be red

`x=2`

`y=4+3+2=9`

substitute

`P=(2)/(9)`

step 3

Find out the probability that the first one will be green and the second one red

Multiply both probabilities

`((1)/(2))((2)/(9))=(1)/(9)=0.11`