Final answer:
The total probability of selecting one white ball and one blue ball from the bag is approximately 0.2450 if balls are drawn without replacement after picking each ball. correct option is D.
Step-by-step explanation:
The probability of selecting one white ball and one blue ball from the bag involves calculating the combined probabilities of two events: picking a white ball first and then a blue ball after (or vice versa), since the order in which these events happen doesn't matter for our final probability. We first determine the probability of each event.
For the first event, the probability of picking a white ball is 10 out of the total number of balls (10+12+13+7+8 = 50), which equals 10/50 or 1/5. Then, regardless of whether the white ball is replaced, the probability of picking a blue ball is 12/50.
If there's no replacement, after one ball is picked, the total number of balls decreases by one. So, if we picked a white ball first, we now have 49 balls left in the bag. Hence, the probability of then picking a blue ball is 12/49.
The combined probability of both events is the product of their individual probabilities:
- Without replacement: P(white, then blue) = (10/50) * (12/49) = 0.1224
To get the total probability of either event happening first, we'd need to multiply this by 2 (since we could also pick a blue then a white ball).
Total Probability = 2 * P(white, then blue) = 2 * 0.1224 = 0.2449
Therefore, the probability of selecting one white ball and one blue ball is approximately 0.2450 when rounded to the nearest ten-thousandth.