Correct question:
An urn holds 3 red and 7 black balls. Players A and B take turns withdrawing balls until a red one is chosen. Calculate the probability that A picks the red ball. (A goes first, followed by B, with no replacement of drawn balls).
Answer:
The likelihood that A picks the red ball is 58.33 %
Step-by-step explanation:
A will select the red ball if it is drawn 1st, 3rd, 5th, or 7th.
1st draw: 9C2
3rd draw: 7C2
5th draw: 5C2
7th draw: 3C2
Calculating for all possible scenarios gives us:
9C2 = (9!) / (7!2!) = 36
7C2 = (7!) / (5!2!) = 21
5C2 = (5!) / (3!2!) = 10
3C2 = (3!) / (2!) = 3
Adding these possibilities results in 36 + 21 + 10 + 3 = 70.
The total outcomes for selecting a red ball = 10C3
10C3 = (10!) / (7!3!)
= 120.
The probability that A selects the red ball is determined by dividing the sum of possible events by the overall outcomes.
P( A selects the red ball) = 70 / 120
= 0.5833
= 58.33 %
