Answer:
The probability that A selects the first red ball is 0.5833.
Step-by-step explanation:
Given : An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively. 
To find : What is the probability that A selects the first red ball? 
Solution : 
A wins if the first red ball is drawn 1st,3rd,5th or 7th.
A red ball drawn first, there are  places in which the other 2 red balls can be placed.
 places in which the other 2 red balls can be placed.
A red ball drawn third, there are  places in which the other 2 red balls can be placed.
 places in which the other 2 red balls can be placed.
A red ball drawn fifth, there are  places in which the other 2 red balls can be placed.
 places in which the other 2 red balls can be placed.
A red ball drawn seventh, there are  places in which the other 2 red balls can be placed.
 places in which the other 2 red balls can be placed.
The total number of total event is  
 
The probability that A selects the first red ball is 



