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ample: An urn fontains 5 green balls, 2 blue balls, and 3 red balls, three balls are removed at random from the win without replecement. If x denote the no. red balls, find p'm.f. of x.

Answer :

The probability that the second ball drawn is red is 25/56.

Let's calculate the probability of the second ball being red.

When the first ball is drawn, there are three possible outcomes: green (G), red (R), or red after adding a red ball (RR). The probabilities of these outcomes are as follows:

P(G) = 2/7 (2 green balls out of a total of 7 balls)

P(R) = 5/7 (5 red balls out of a total of 7 balls)

P(RR) = (5/7) * (6/8) = 15/28 (since the probability of drawing a red ball and then adding another red ball is (5/7) * (6/8))

Now, to find the probability of drawing a red ball as the second ball, we consider two cases:

Case 1: The first ball drawn is green (G).

In this case, the probability of drawing a red ball as the second ball is P(R|G) = 5/8 (5 red balls out of 8 total balls remaining).

Case 2: The first ball drawn is red (R) or red after adding a red ball (RR).

In these cases, the probability of drawing a red ball as the second ball is P(R|R) = 6/8 (6 red balls out of 8 total balls remaining).

Now, we calculate the overall probability using the law of total probability:

P(R) = P(G) * P(R|G) + P(RR) * P(R|R)

= (2/7) * (5/8) + (15/28) * (6/8)

= 10/56 + 90/224

= 100/224

= 25/56

Therefore, the probability that the second ball drawn is red is 25/56.

For more information on probability visit: brainly.com/question/29588226

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