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.)

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).

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 %