Question

A box contains different colored paper clips. The probability of drawing two red paper clips from the box without replacement is 1/7, and the probability of drawing one red paper clip is 2/5.What is the probability of drawing a second red paper clip, given that the first paper clip is red?1/65/142/32/35

Answer 1

The probability of two red paper clips without replacement means

The probability of drawing the first and the probability of drawing the second one. This is represented as

`P(R_(1st)\cap R_(2nd))`

And this was given as

`(1)/(7)`

So

`P(R_(1st)\cap R_(2nd))=(1)/(7)`

Probalilty of drawing one red paper clip is

`P(R_(1st))=(2)/(5)`

Now the probability of drawing a second red paper clip, given that the first paper clip is red becomes

`\begin{gathered} P(R_(1st)/R_(2nd))=(P(R_(1st)\cap R_(2nd)))/(P(R_(1st))) \\ \\ P(R_(1st)/R_(2nd))=((1)/(7))/((2)/(5)) \\ \\ =(5)/(14) \end{gathered}`