A box contains 12 marbles, of which 5 are green. All are indishtinguishable in size and in weight and have equal probability of being chosen. Without looking, three are selected and placed in a box. What is the probability that all 3 are green?
2007-05-14 18:55:44 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The chance that the first marble is green is 5/12.
After the first marble is removed (presumably green), there are 4 green marbles left and 11 marbles total. The chance the second marble is green is 4/11.
After the second marble is removed (presumably green again), there are 3 green marbles left and 10 marbles total. The chance the third marble is green is 3/10.
We multiply these three numbers together:
5/12 * 4/11 * 3/10
= 60/1320
= 1/22
= 0.04545.....
Or you could do it permutationally:
Selecting 3 from 5
5P3
=5*4*3
=60
Selecting 3 from 12
12P3
=12*11*10
=1320
Basically this is ways to select 3 green marbles and ways to select 3 marbles. So what you want is 3 green marbles divide three marbles:
60/1320
= 1/22
= 0.04545.....
Which is the same!
2007-05-14 19:02:09 · answer #1 · answered by Anonymous · 1⤊ 0⤋
P(1st to be green) equals 5/12
now in the box, 4 green remain and total 11 remain
P(2nd green) equals 4/11
similarily P(3rd green) equals 3/10
so P(all 3 green) equals 5/12 * 4/11 * 3/10 which is 1/22
2007-05-14 19:03:28 · answer #2 · answered by Anonymous · 0⤊ 0⤋
5/12 • 4/11 • 3/10 = 1/22
2007-05-14 19:02:54 · answer #3 · answered by Philo 7 · 0⤊ 0⤋
If you pick a blue first the probability is 2/8, and the probability of picking a second blue is 1/7 So the probability of picking 2 blues is 2/8 x 1/7 = 2 in 56 Because there are the same amount of black balls as blue ones the probability of picking 2 black ones is also 2 in 56 If you pick a white ball first the probability is 4/8, and the probability of picking a second white is 3/7. So the probability of picking 2 whites is 4/8 x 3/7 = 12 in 56 So the chances of picking 2 balls the same is 2/56 + 2/56 + 12/56 = 16/56 = 2/7
2016-05-18 04:54:03 · answer #4 · answered by ? 4 · 0⤊ 0⤋
The ways of selecting 3 green marbles out of 5 and the balls are indistinguishable can be done in 1 ways
and
The total number of ways of selecting 3 marbles out of 12 = 12C3 = 220
Therefore the required probability will be = 1/220
2007-05-14 19:08:57 · answer #5 · answered by ritesh s 2 · 0⤊ 0⤋
there are 5 green and 7 of other colors
probability to chose the first green is 5/12
probability to chose the second green is 4/11
probability to chose the third green is 3/10
the probability is 5/12*4/11*3/10
= .0454545(45/990)
2007-05-14 19:06:42 · answer #6 · answered by lilmaninbigpants 3 · 0⤊ 0⤋
those answers are correct, but here is a different way to do it
(5 c 3) (7 c 0)/ (12 c 3)=
(10) (1)/ 220= 1/22
2007-05-14 19:10:27 · answer #7 · answered by James O only logical answer D 4 · 0⤊ 0⤋