What Is the Probability of Drawing One White and One Green Marble?

[nesan]

Homework Statement

Two bags contain marbles.

Bag A contains 2 white marbles and 2 green marbles.

Bag B contains 3 white marbles, 5 red marbles, and 4 green marbles.

If you draw one marble at random from each bag, what is the probability of drawing 1 white marble and 1 green marble?

I AM STUCK. :|

Help please.

Homework Equations

Independent and dependent events.

The Attempt at a Solution

Event A = Drawing 1 white marble

Event B = drawing 1 green marble

p(A) = 2 / 4
p(B) = 4 / 12

2 / 4 * 4 / 12 = 8 / 48

For some reason it doesn't seem right to me, too easy. ._.

 

[klawlor419]

I think it would be 5/16+6/16 = 11/16. It doesn't matter which bags the marbles come from as long as you have 1 white and 1 green in your hands.

 

[lurflurf]

no

Either do
(probability bag B draw is not red)(probability bag A draw is opposite bag B draw)
or
consider all cases (there are only 48)

 

[Ray Vickson]

Homework Statement

Two bags contain marbles.

Bag A contains 2 white marbles and 2 green marbles.

Bag B contains 3 white marbles, 5 red marbles, and 4 green marbles.

If you draw one marble at random from each bag, what is the probability of drawing 1 white marble and 1 green marble?

I AM STUCK. :|

Help please.

Homework Equations

Independent and dependent events.

The Attempt at a Solution

Event A = Drawing 1 white marble

Event B = drawing 1 green marble

p(A) = 2 / 4
p(B) = 4 / 12

2 / 4 * 4 / 12 = 8 / 48

For some reason it doesn't seem right to me, too easy. ._.

The individual sample points are:
WG = white from bag A and green from bag B
GW = green from bag A and white from bag B
(so the first letter is for bag A and the second is for bag B).

The event you want is E = {WG,GW}, so P{E} = P(WG) + P(GW).

How would you compute P(WG) and P(GW)?

RGV

 

[HallsofIvy]

Homework Statement

Two bags contain marbles.

Bag A contains 2 white marbles and 2 green marbles.

Bag B contains 3 white marbles, 5 red marbles, and 4 green marbles.

If you draw one marble at random from each bag, what is the probability of drawing 1 white marble and 1 green marble?

I AM STUCK. :|

Help please.

Homework Equations

Independent and dependent events.

The Attempt at a Solution

Event A = Drawing 1 white marble

Event B = drawing 1 green marble

p(A) = 2 / 4
p(B) = 4 / 12

2 / 4 * 4 / 12 = 8 / 48

For some reason it doesn't seem right to me, too easy. ._.

You are right- both in what you have done and that you are not done yet. That's the probability of drawing a whit marble from bag A and and green marble from bag B. But now you have to do it the other way around. There are 4 marbles in bag A and 2 of them are green so the probability of drawing a green marble from bag A is 2/4= 1/2. There are 12 marbles in bag B and 3 of the are white so the probability of drawing a white marble from bag B is 3/12= 1/4. The probability of drawing "a green marble from bag A and a white marble from bag B is (1/2)(1/4)= 1/8.