Question

There are 8 black balls and 7 red balls in an urn. If 5 balls are drawn without replacement, what is the probability that exactly 3 black balls are drawn? Express youranswer as a fraction or a decimal number rounded to four decimal places.AnswerHow to enter your answer (opens in new window)KeypadKeyboard ShortcutsTables

Answer 1

Step-by-step explanation:

The number of black balls is

`n(B)=8`

The number of red balls is

`n(R)=7`

The total number of balls are

`totalballs=8+7=15`

Step 1:

Calculate the numerator

The number of ways to choose 3 black from 8 black balls is given below as

`\begin{gathered} 8C3 \\ =56ways \end{gathered}`

We will then choose the remaining 2 red balls from the 7 red balls below as

`\begin{gathered} 7C2 \\ 21ways \end{gathered}`

Therefore,

The numerator will be

`\begin{gathered} 56*21 \\ =1176 \end{gathered}`

Step 2:

Calculate the denominator

Here we are going to calculate the number of ways to choose 5 balls from a total of 15 balls below as

`\begin{gathered} 15C5 \\ =3003 \end{gathered}`

Therefore,

The probability of picking exactly 3 black balls will be

`\begin{gathered} (1176)/(3003) \\ (56)/(143) \end{gathered}`

Hence,

The final answer is

`\Rightarrow(56)/(143)`