Question

There are 6 red balls & 8 green balls in a bag. 5 balls are drawn out at random & placed in a red box; the remaining 9 balls are put in a green box. What is 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?

• A. $213/1001$
• B. $48/1001$
• C. $165/1001$
• D. None of the above

Answer 1

The correct option is A $213/1001$

Red Box		Green Box
Red	Green	Green	Red
5	0	8	1	$\to$ Non-prime
4	1	7	2
3	2	6	3
2	3	5	4
1	4	4	5	$\to$ Non-prime
0	5	3	6

Required probability $=\frac{{}^6{C}_5{.}^8{C}_0{+}^6{C}_1{.}^8{C}_4}{{}^{14}{C}_5}=\frac{213}{1001}$