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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
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B
48/1001
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C
165/1001
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D
None of the above
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Solution

The correct option is A 213/1001
Red Box

Green Box


Red
Green
Green
Red

5
0
8
1
Non-prime
4
1
7
2

3
2
6
3

2
3
5
4

1
4
4
5
Non-prime
0
5
3
6

Required probability =6C5.8C0+6C1.8C414C5=2131001

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