Question

There are eight black balls and six red balls in an urn if 5 balls are drawn with out replacement what is the probability that exactly one black ball is drawn express your answer as a fraction or decimal number rounded to four decimal places

Answer 1

Step-by-step explanation:

The number of black balls is

`n(B)=8`

The number of red balls in the urn is

`n(R)=6`

The total number of balls will be calculated as

`\begin{gathered} n(S)=n(B)+n(R) \\ n(S)=8+6 \\ n(S)=14 \end{gathered}`

Step 1:

Get the numerator

To do this, we will have to choose one black from the 8 black balls below as

`\begin{gathered} 8C1= \\ =8ways \end{gathered}`

We will now choose the reamining balls from the 6 red balls which will give us

`\begin{gathered} 6C4 \\ =15 \end{gathered}`

Hence,

The numerator will be

`8*15=120`

Step 2:

We will get the deonminator below as

Choosing 5 balls from 14

`\begin{gathered} 14C5 \\ =2002 \end{gathered}`

Therefore,

the probability og picking exactly one ball will be

`\begin{gathered} (120)/(2002) \\ =(60)/(1001) \end{gathered}`

Hence,

The Probability that exactly 1 black ball is drawn will be

`\Rightarrow(60)/(1001)`