An urn contains 3 red and 7 black balls.



Answered 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 & Explanation



Skilled2021-08-19Added 88 answers

A wins if the first red ball is drawn on the first, third, fifth, or seventh.
We'll count the number of times a red ball appears for the first time. (For example, if a red ball is drawn first, there are (9C2) spots where the other two red balls can be placed. To put it another way, there are (9C2) instances in which A wins on the first draw).
When the sum up the number of favorable events and divide by the number of total events. 
E(x): The number of positive events (position of the first red ball)
S: Total number of occurrences (all possible combinations of the balls)
P(A wins)=(9C2)+(7C2)+(5C2)+(3C2)10C3 
P(A wins)=.05833

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