Geoff is running a carnival game. he has 15 marbles in a bag: there are 3 green marbles, 7 red marbles and 5 yellow marbles. to play a round of the game, a player randomly takes out a marble from the bag, notes the color and replaces it, then pulls a second marble from the bag and notes the color. so in effect, the player pulls 2 marbles from the bag. (however, the first marble is put back in the bag and so potentially could be pulled twice.) green marbles win 5 points, red marbles win 2 point and yellow marbles lose 2 points let x be the random variable that describes the number of points won by a player playing a single round of geoff's marble game. find the probability distribution for x. give values for x as whole numbers and probabilities as decimal values to 3 decimal places. enter the values for x in ascending order (lowest to highest) from left to right in the table.

given below

Step-by-step explanation:

given that he has 15 marbles in a bag: there are 3 green marbles, 7 red marbles and 5 yellow marbles.

To play a round of the game,a player randomly takes out a marble from the bag, notes the color and replaces it, then pulls a second marble from the bag and notes the color.

P(Green) =

P(Red) =

P(Yellow) =

since each time replaced the prob for I and II draw remains the same.

X=the random variable that describes the number of points won by a player playing a single round of Geoff's marble game.

If best he drawn 2 green there x=10, the worst is he draws two yellow and loses 4, if two red gain is 4 points

The different ways are 2 green, 2 red, 2 yellow, (1r,1g) (g,y) (y,r)

Events  (y,y)         (y,r)     (y,g)         (r,r)      (r,g)    (g,g)  -- 6 number of ways

X =           -4,         0           3            4         7            10

Pr             0.111    0.312  0.133    0.218   0.186       0.04

Whenever we have y,r i.e. change of colour we multiply by 2 because it can be y,r or r,y

The above is pdf of X

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