Four red balls and two white balls are placed in a jar. One ball is randomly removed and replaced with a ball of the other color. The jar is then shaken, and one ball is randomly selected. What is the probability that this ball is red? Express your answer as a common fraction.
11/18
To determine the probability of selecting a red ball, we need to first calculate the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Initially, there are 6 balls in the jar (four red and two white). After one ball is removed and replaced with a ball of the other color, there are still 6 balls in the jar, but the color distribution may have changed. Therefore, the total number of possible outcomes remains the same, which is 6.
Number of favorable outcomes:
There are two scenarios in which we will have a red ball:
1) If initially a red ball is chosen and replaced with a white ball (probability: 4/6 * 2/6 = 8/36).
2) If initially a white ball is chosen and replaced with a red ball (probability: 2/6 * 4/6 = 8/36).
Therefore, the number of favorable outcomes is (8/36) + (8/36) = 16/36.
The probability of selecting a red ball is given by the ratio of favorable outcomes to the total number of outcomes:
Probability of selecting a red ball = (Number of favorable outcomes) / (Total number of outcomes)
Probability of selecting a red ball = (16/36) / 1
Probability of selecting a red ball = 16/36
So, the probability of selecting a red ball is 16/36, which can be simplified to 4/9.