An urn contains 3 red and 7 black balls. Players and withdraw balls from the urn consecutively until a red ball is selected. Find the probability that selects the red ball. (draws the first ball, then and so on. There is no replacement of the balls drawn.)

Question

Mathematics

Kenyon Blackwell

13 September, 01:26

An urn contains 3 red and 7 black balls. Players and withdraw balls from the urn consecutively until a red ball is selected. Find the probability that selects the red ball. (draws the first ball, then and so on. There is no replacement of the balls drawn.)

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Answers (1)

Know the Answer?

Sanaa Jensen · Answer 1

Correct question:

An urn contains 3 red and 7 black balls. Players A and B withdraw balls from the urn consecutively until a red ball is selected. Find the probability that A selects the red ball. (A draws the first ball, then B, and so on. There is no replacement of the balls drawn).

Answer:

The probability that A selects the red ball is 58.33 %

Step-by-step explanation:

A selects the red ball if the first red ball is drawn 1st, 3rd, 5th or 7th

1st selection: 9C2

3rd selection: 7C2

5th selection: 5C2

7th selection: 3C2

9C2 = (9!) / (7!2!) = 36

7C2 = (7!) / (5!2!) = 21

5C2 = (5!) / (3!2!) = 10

3C2 = (3!) / (2!) = 3

sum of all the possible events = 36 + 21 + 10 + 3 = 70

Total possible outcome of selecting the red ball = 10C3

10C3 = (10!) / (7!3!)

= 120

The probability that A selects the red ball is sum of all the possible events divided by the total possible outcome.

P (A selects the red ball) = 70 / 120

= 0.5833

= 58.33 %