Question

4) A bag contains 20 marbles, four are red, five are green, three are yellow, and eight are blue. If you choosetwo marbles, without replacing the first one after you draw it, what is the probability of you choosing a redand then a green marble?

Answer 1

Step-by-step explanation:

Given;

We are given the following information;

A bag contains 20 marbles. Of these, the colors are as follows;

`\begin{gathered} Red=4 \\ Green=5 \\ Yellow=3 \\ Blue=8 \\ Total=20 \end{gathered}`

Required;

We are required to find the probability that a marble chosen at random will be red and then another one blue (without replacement).

Step-by-step solution;

To solve this we need to first bear in mind the formula for calculating the probability of an event.

`P[Event]=\frac{Number\text{ }of\text{ }required\text{ }outcomes}{Number\text{ }of\text{ }possible\text{ }outcomes}`

For this experiment, the number of all possible outcomes is 20.

Therefore, the probability of drawing a red marble will be;

`\begin{gathered} P[Red]=(4)/(20) \\ \\ P[red]=(1)/(5) \end{gathered}`

Remember we are told that the first marble is drawn and then, without replacement a second one is drawn. Without replacement indicates that we now have 19 marbles left in the bag. Hence, the number of possible outcomes is now 19 (and no longer 20).

So, the probability of drawing a green marble will be;

`P[Green]=(5)/(19)`

Now we have two probabilities. The probability of a red marble and then a green marble. This is a product of probabilities.

Therefore, the probability of choosing a red and then a green marble will be;

`\begin{gathered} P[Red]\text{ }and\text{ }P[Green]=(1)/(5)*(5)/(19) \\ \\ P[Red]\text{ }and\text{ }P[Green]=(1)/(19) \end{gathered}`

ANSWER:

The probability of choosing a red and then a green marble will be

`(1)/(19)`