Problem Solving

A bag contains six marbles: two red, two blue, and two green. If two marbles are drawn at random, what is the probability that they are the same color?

oa: [spoiler]1/5[/spoiler]

i keep on getting 1/15???

how should i tackle these pair problems.

Prob. of getting two red balls = 2C2/6C2 = 1/15

p(2 blue balls) = p(2 green balls) = 1/15

Prob of getting 2 balls of the same color = 1/15 + 1/15 + 1/15 = 1/5

Gurpinder wrote:A bag contains six marbles: two red, two blue, and two green. If two marbles are drawn at random, what is the probability that they are the same color?

oa: [spoiler]1/5[/spoiler]

i keep on getting 1/15???

how should i tackle these pair problems.

Total way to select 2 marbles 6!/4!2!=15
Fav way to select 2 marble 3 only 3 set of same color marble.

Prob = 3/15 = 1/5

nithi_mystics wrote:Prob. of getting two red balls = 2C2/6C2 = 1/15

p(2 blue balls) = p(2 green balls) = 1/15

Prob of getting 2 balls of the same color = 1/15 + 1/15 + 1/15 = 1/5

but doesent the problem say that you pick 2 balls at random. so doesent that mean that your choice on the first ball will effect the options for the next selection. thats what i was doing.

1/3 for 1st selection.
1/5 for 2nd selection

= 1/15

Just think of it this way, it doesn't matter what color you chose first, so ignore that.
No suppose you chose any color, what is the probability of choosing a match....1/5
Because you have one marble that will match that selection out of a total of 5 marbles left.

jeffedwards wrote:Just think of it this way, it doesn't matter what color you chose first, so ignore that.
No suppose you chose any color, what is the probability of choosing a match....1/5
Because you have one marble that will match that selection out of a total of 5 marbles left.

what if the ratio of color of balls was different?

Gurpinder wrote:

jeffedwards wrote:Just think of it this way, it doesn't matter what color you chose first, so ignore that.
No suppose you chose any color, what is the probability of choosing a match....1/5
Because you have one marble that will match that selection out of a total of 5 marbles left.

what if the ratio of color of balls was different?

Good question

Then you would have to do the probability separate. So in this case you would solve the problem just as nithi_mystics.

Probability of red 2/6 or 1/3
Probability of red again 1/5
Times it (1/3)*(1/5) = 1/15 (That's the probability of drawing red and red again)
Repeat the process for all three colors and add the results
(1/15)+ (1/15)+ (1/15) = 3/15 = 1/5
1/5 is your answer