Question bank/JEE Main/Mathematics
JEE MainMathematicsEasy / Moderate/ ToughProbability
There are 6 red balls and 6 green balls in a bag. Five balls are
drawn out at random and placed in a red box. The remaining seven balls
are put in a green box. If 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 where p and q are relatively prime, then
find the value of (p + q),d cSx esa 6 yky xSans rFkk 6 gjh xSans gSA ik¡p xSanksa dks yky cDlsa;fn yky cDlsa esa gjh xSanksa rFkk gjs cD yky xSanksa tgk¡ p rFkk q ijLij rc (p + q)
Show answer and solution
6R and 6G
5 Ball in Red box
7 Ball in Green box
Red box Green box sum of G from red box and R from Green box
1G, 4R 5G, 2R 3 ×
2G, 3R 4G, 3R 5 ×
3G, 2R 3G, 4R 7 ×
4G, 1R 2G, 5R 9 √
5G, 0R 1G, 6R 11 ×
5R, 0R 6G, 1R 1 √
Total = ^12C_5
Favourable = ^6C_4. ^6C_1 + ^6C_5. ^6C_0
Probability
p + q = 37
5 Ball in Red box
7 Ball in Green box
Red box Green box sum of G from red box and R from Green box
1G, 4R 5G, 2R 3 ×
2G, 3R 4G, 3R 5 ×
3G, 2R 3G, 4R 7 ×
4G, 1R 2G, 5R 9 √
5G, 0R 1G, 6R 11 ×
5R, 0R 6G, 1R 1 √
Total = ^12C_5
Favourable = ^6C_4. ^6C_1 + ^6C_5. ^6C_0
Probability
p + q = 37
Source: Grass-G / M-21 Mathematics Paper 19 Dec Hindi Eng.docx
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