Question

There are 10 black balls and eight red balls in an urn. If four balls are drawn without replacement what is the probability that exactly 2 blackballs are drawn? Express your answer as a fraction or decimal number rounded to four decimal places

Answer 1

Solution:

Given that there are 10 black balls and 8 red balls in an urn, this implies that

$\begin{gathered} n(Total)=n(black)+n(red) \\ 18=10+8 \end{gathered}$

Given that 4 balls are drawn without replacement, where exactly 2 black balls are drawn, this implies that

$\begin{gathered} number\text{ of ways of selecting 2 black balls:} \\ 10C2\text{ = 45 ways} \\ number\text{ of ways selecting the remaining balls from the the 8 red balls:} \\ 8C2=\text{ 28 ways} \end{gathered}$

This gives

$\begin{gathered} Probability\text{ of selecting exactly 2 balck balls = }\frac{45\times28}{18C4} \\ =\frac{45\times28}{3060} \\ =\frac{7}{17} \\ =0.4118(4\text{ decimal places\rparen} \end{gathered}$