Difficult Math Problem #14

[800guy]

OA coming after a few people answer

Kurt, a painter, has 9 jars of paint:
4 are yellow
2 are red
rest are brown
Kurt will combine 3 jars of paint into a new container to make a new color, which he will name accordingly to the following conditions:

Brun Y if the paint contains 2 jars of brown paint and no yellow
Brun X if the paint contains 3 jars of brown paint
Jaune X if the paint contains at least 2 jars of yellow
Jaune Y if the paint contains exactly 1 jar of yellow

What is the probability that the new color will be Jaune

a) 5/42
b) 37/42
c) 1/21
d) 4/9
e) 5/9

[gamemaster]

my solution:

ill define: Y - Yellow NY = not yellow, so the probabilites are:

Y NY NY = 4/9 * 5/8 * 4/7
NY Y NY = 5/9 * 4/8 * 4/7
NY NY Y = 5/9 * 4/8*4/7

for 2, they say AT LEAST 2 so:

Y Y NY = 4/9*3/8*1 <<<< because it can be 2 or 3
Y NY Y = 4/9*5/8*3/7
NY Y Y = 5/9*4/8*3/7

finally you have to sum it all up, i didnt do it because im lasy

[nguyen_thiet_thanh]

Total possibility of taking 3 jars from 9 jar is 84 (=9!/3!*6!)
The Jaune possibility is
for at least 2 Yellow: 30 (2 Yellow) + 4 (3 yellow)
for 1 yellow = 40
so the possibility is 74/84 = 37/42 (B)

[800guy]

here's the OA:

This has at least 2 yellow meaning..

a> there can be all three Y => 4c3
OR
b> 2 Y and 1 out of 2 R and 3 B => 4c2 x 5c1

Total 34

2.This has exactly 1 Y and remaining 2 out of 5 = > 4c1 x 5c2

Total 40
Total possibilities = (9!/3!6!) = 84
Adding the two probabilities: probability = 74/84 = 37/42