Final answer:
To find the number of white marbles Daniel put in the sack, we can set up an equation based on the probability of picking a red marble. The number of white marbles will be 5. The probability of not picking a blue or white marble is 10 / (13 + x).
Step-by-step explanation:
To find the number of white marbles Daniel put in the sack, we need to determine the total number of marbles in the sack. From the given information, we know that Daniel took 4 red marbles, 6 green marbles, and 3 blue marbles. Let's assume the number of white marbles is x. Therefore, the total number of marbles will be 4 + 6 + 3 + x = 13 + x.
Given that the probability of picking a red marble is 2/9, we can set up the equation:
4 / (13 + x) = 2 / 9
Cross multiplying, we get:
2(13 + x) = 4 * 9
Simplifying, we have:
26 + 2x = 36
2x = 36 - 26
2x = 10
x = 5
Hence, Daniel put 5 white marbles in the sack.
To find the probability of not picking a blue or white marble from the sack, we need to determine the total number of marbles in the sack. From the given information, we know that Daniel took 4 red marbles, 6 green marbles, 3 blue marbles, and x white marbles. Therefore, the total number of marbles will be 4 + 6 + 3 + x.
The probability of not picking a blue or white marble is equal to the probability of picking a red or green marble.
The probability of picking a red marble is 4 / (13 + x), and the probability of picking a green marble is 6 / (13 + x). Adding these probabilities, we get:
(4 + 6) / (13 + x) = 10 / (13 + x)
Hence, the probability of not picking a blue or white marble from the sack is 10 / (13 + x).