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In a certain carnival game the player selects two balls at random from an urn containing 3 red balls and 9 white balls. The player receives $4 if he draws two red balls and $1 if he draws one red ball. He loses $2 if no red balls are in the sample. Determine the probability distribution for the experiment of playing the game and observing the player's earnings.
The probability to draw two red balls is __, to draw one red ball is __, and to draw zero red balls is __.

Respuesta :

Answer:

The probability to draw two red balls = 1/22

The probability to draw one red ball = 9/22

The probability to draw no red ball = 12/22

Step-by-step explanation:

Number of Red balls = 3

Number of White balls = 9

If the player draws two red balls, he receives $4

If the player draws one red ball, he receives $1

If the player draws no red ball, he looses $2

The total number of balls = 3+9

= 12

Let R represent Red balls

Let W represent White balls

The probability that the player earns $4 by picking two red balls is represented as Pr(R1 n R2)

Pr(R1 n R2) = Pr(R1) * Pr(R2)

Pr(R1) = 3/12

= 1/4

Pr(R2) = 2/11(we assume he draws without replacement)

Pr(R1 n R2) = 1/4*2/11

= 2/44

= 1/22

The probability of earning $4 is 1/22

The probability of drawing one red ball is Pr(R1 n W2) or Pr(W1 n R2)

Pr(R1) = 3/12

= 1/4

Pr(W2) = 9/11

Pr(W1) = 9/12

= 3/4

Pr(R2) = 3/11

Pr(R1 n W2) or Pr(W1 n R2) =

(1/4 * 9/11) + (3/4 * 3/11)

= (9/44) + (9/44)

= 18/44

= 9/22

Therefore, the probability of earning $1 is 9/22

The probability that no red ball is chosen is Pr(W1nW2)

Pr(W1) = 9/12

= 3/4

Pr(W2) = 8/12

Pr(W1nW2) = 3/4 * 8/11

= 24/44

= 12/22

therefore. the probability of loosing $2 is 12/22

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