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Hello! I need help on yet another probability question..

Question:

A red dice has the number 1 on one face, the number 2 on two faces and the number 3 on three faces. Two green dice each has the number 6 on one face and the number 5 on five faces. The three dice are thrown together.

Calculate the probability of obtaining 2 on the red dice, 5 and 6 on the two green dice.

I know that...

P(2 on red dice)= 2/6

P(5 and 6 on the two green dice)

= 2(5/6 X 1/6)

= 5/18

But here's where my confusion sprouts from. The different possible outcomes are:

2 on red, 5 on G-1 and 6 on G-2, or

2 on red, 5 on G-2 and 6 on G-1.

where G-1 and G-2 are the green dices.

I'm not sure if

(A)I should count the "2 on red" once, since the events for the red dice are independent of the other dices,i.e.

P(obtaining 2 on red,5 and 6 on green dice)

= 2/6 X 5/18

= 5/54

Or (B)Add the probabilities of the possible outcomes together, which will get me...

P(obtaining 2 on red,5 and 6 on green dice)

= 2(2/6 X 5/18)

= 5/27

Sorry if this post is confusing..

Question:

A red dice has the number 1 on one face, the number 2 on two faces and the number 3 on three faces. Two green dice each has the number 6 on one face and the number 5 on five faces. The three dice are thrown together.

Calculate the probability of obtaining 2 on the red dice, 5 and 6 on the two green dice.

I know that...

P(2 on red dice)= 2/6

P(5 and 6 on the two green dice)

= 2(5/6 X 1/6)

= 5/18

But here's where my confusion sprouts from. The different possible outcomes are:

2 on red, 5 on G-1 and 6 on G-2, or

2 on red, 5 on G-2 and 6 on G-1.

where G-1 and G-2 are the green dices.

I'm not sure if

(A)I should count the "2 on red" once, since the events for the red dice are independent of the other dices,i.e.

P(obtaining 2 on red,5 and 6 on green dice)

= 2/6 X 5/18

= 5/54

Or (B)Add the probabilities of the possible outcomes together, which will get me...

P(obtaining 2 on red,5 and 6 on green dice)

= 2(2/6 X 5/18)

= 5/27

Sorry if this post is confusing..

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