To determine the probability of choosing two white chips in succession from a bag containing 4 white chips and 6 black chips, we can follow these steps:
Initially, there are a total of 10 chips in the bag (4 white and 6 black).
1. **Probability of the first white chip**: The probability of drawing a white chip first is the number of white chips divided by the total number of chips. This can be calculated as:
P(First White) = Number of White Chips / Total Chips = 4 / 10 = 2 / 5
2. **Removing the first chip**: Once we have drawn one white chip, we do not replace it. Now, there are only 3 white chips left and the total number of chips is now 9 (3 white and 6 black).
3. **Probability of the second white chip**: The probability of drawing a second white chip now becomes:
P(Second White | First White) = Number of Remaining White Chips / Total Remaining Chips = 3 / 9 = 1 / 3
4. **Calculating the overall probability**: To get the total probability of both events happening (choosing a white chip first and then another white chip), we multiply the probabilities of each event:
P(Both White) = P(First White) * P(Second White | First White)
P(Both White) = (2 / 5) * (1 / 3) = 2 / 15
Thus, the probability of randomly choosing a white chip, not replacing it, and then randomly choosing another white chip is 2/15.