Question

There are 6 red balls and 8 green balls in a bag. 5 balls are drawn at random and placed in a red box, the remaining 9 balls are put in a green box. The probability that the number of red balls in the green box plus the number of green balls in the red box is not a prime number is

• A. $\frac{213}{1001}$
• B. $\frac{1}{2}$
• C. $\frac{215}{1001}$
• D. $\frac{11}{663}$

Answer 1

The correct option is A $\frac{213}{1001}$

$\begin{array}{cc}RedBox& GreenBox\\ 5R& 1R8G\to Favourable\\ 4R1G& 2R7G\\ 3R2G& 3R6G\\ 2R3G& 4R5G\\ 1R4G& 5R4G\to Favourable\\ 5G& 6R3G\end{array}$
$\therefore Probability=\frac{{}^6{C}_5{+}^6{C}_1{\times }^8{C}_4}{{}^{14}{C}_5}=\frac{213}{1001}$