Wo balls are chosen randomly from an um containing 8 white, 4 black, and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1for each white ball selected. LetXdenote our winnings. What are the possible valuesofX, and what are the probabilities associated with each value

The probability distribution is shown below.

Step-by-step explanation:

The urn consists of 8 white (W), 4 black (B) and 2 orange (O) balls.

The winning and losing criteria are:

There are 8 + 4 + 2 = 14 balls in the urn.

The number of ways to select two balls is, ways.

The distribution of amount won or lost is as follows:

Outcomes: WW  WO  WB  BB  BO  OO

X:                 -2      -1      1      4     2      0

Compute the probability of selecting 2 white balls as follows:

The number of ways to select 2 white balls is, ways.

The probability of WW is,

Compute the probability of selecting 1 white ball and 1 orange ball as follows:

The number of ways to select 1 white ball and 1 orange ball is, ways.

The probability of WO is,

Compute the probability of selecting 1 white ball and 1 black ball as follows:

The number of ways to select 1 white ball and 1 black ball is, ways.

The probability of WB is,

Compute the probability of selecting 2 black balls as follows:

The number of ways to select 2 black balls is, ways.

The probability of BB is,

Compute the probability of selecting 1 black ball and 1 orange ball as follows:

The number of ways to select 1 black ball and 1 orange ball is, ways.

The probability of BO is,

Compute the probability of selecting 2 orange balls as follows:

The number of ways to select 2 orange balls is, ways.

The probability of OO is,

The probability distribution of X is:

Outcomes:    WW     WO        WB         BB        BO         OO

X:                    -2          -1            1            4            2            0

P (X):           0.3077  0.1758  0.3516  0.0659  0.0879  0.0110

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step-by-step explanation:

step-by-step explanation: