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

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

$8\times15=120$

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

$\begin{gathered} \frac{120}{2002} \\ =\frac{60}{1001} \end{gathered}$

Hence,

The Probability that exactly 1 black ball is drawn will be

$\Rightarrow\frac{60}{1001}$