Question 1170030: An urn contains two blue balls (denoted B1 and B2) and three white balls (denoted W1, W2, and W3). One ball is drawn from the urn, its color recorded, and is replaced. Another ball is then drawn and its color recorded.
Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment on a sheet of paper.
Consider the event that the first ball that is drawn is blue. Count all the outcomes in this event.
What is the total?
What is the probability of the event?
(b)
Consider the event that only white balls are drawn. Count all the outcomes in this event.
What is the total?
What is the probability of the event?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step by step.
**1. List All Possible Outcomes:**
The urn contains: B1, B2, W1, W2, W3.
Since we draw a ball, replace it, and draw again, there are 5 possible outcomes for the first draw and 5 for the second draw. This gives us 5 * 5 = 25 possible outcomes.
The possible outcomes are:
* B1B1, B1B2, B1W1, B1W2, B1W3
* B2B1, B2B2, B2W1, B2W2, B2W3
* W1B1, W1B2, W1W1, W1W2, W1W3
* W2B1, W2B2, W2W1, W2W2, W2W3
* W3B1, W3B2, W3W1, W3W2, W3W3
**2. Event: First Ball Drawn is Blue**
* Count the outcomes where the first ball is blue:
* B1B1, B1B2, B1W1, B1W2, B1W3
* B2B1, B2B2, B2W1, B2W2, B2W3
* Total outcomes in this event: 10
* Probability of the event:
* Probability = (Number of outcomes in the event) / (Total number of outcomes)
* Probability = 10 / 25 = 2/5 = 0.4
**(a) Answers:**
* Total: 10
* Probability: 2/5 or 0.4
**3. Event: Only White Balls Are Drawn**
* Count the outcomes where both balls drawn are white:
* W1W1, W1W2, W1W3
* W2W1, W2W2, W2W3
* W3W1, W3W2, W3W3
* Total outcomes in this event: 9
* Probability of the event:
* Probability = (Number of outcomes in the event) / (Total number of outcomes)
* Probability = 9 / 25 = 0.36
**(b) Answers:**
* Total: 9
* Probability: 9/25 or 0.36
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