Answer:
Let's denote the probability of drawing a red marble as \( P(R) \), the probability of drawing a green marble as \( P(G) \), and the probability of drawing a yellow marble as \( P(Y) \).
From the given information, we know that:
1. The probability of not drawing a red marble is \( \frac{1}{2} \). This means the probability of drawing a red marble is \( 1 - \frac{1}{2} = \frac{1}{2} \). So, \( P(R) = \frac{1}{2} \).
2. The probability of not drawing a green marble is \( \frac{2}{3} \). This means the probability of drawing a green marble is \( 1 - \frac{2}{3} = \frac{1}{3} \). So, \( P(G) = \frac{1}{3} \).
Since the jar contains only red, green, and yellow marbles, the sum of the probabilities of drawing these three colors should be 1:
\[ P(R) + P(G) + P(Y) = 1 \]
\[ \frac{1}{2} + \frac{1}{3} + P(Y) = 1 \]
\[ \frac{5}{6} + P(Y) = 1 \]
\[ P(Y) = 1 - \frac{5}{6} \]
\[ P(Y) = \frac{1}{6} \]
Therefore, the probability of drawing a yellow marble is \( \frac{1}{6} \).
Answer:
There is a 1/6 probability of drawing a yellow marble.
Step-by-step explanation:
The probability of not drawing a red marble is 1/2, so 1/2 of the marbles must be red. The probability of not drawing a green marble is 2/3, so 1/3 of the marbles must be green. All the rest of the marbles are yellow, so the probability of drawing a yellow marble can be found by subtracting 1/2 and 1/3 from 1.
1 - 1/2 = 1/2
1/2 - 1/3 = ?
Before we can subtract 1/3 from 1/2, we need to convert the two fractions so they have the same denominator. To do this, we must find the Least Common Denominator. To find the LCD, list the multiples of each denominator until a common one is found.
2 -- 2, 4, 6
3 -- 3, 6
The LCD between 2 and 3 is 6. To convert the fractions, multiply the numerator and denominator by the same number.
1/2 * 3/3 = 3/6
1/3 * 2/2 = 2/6
Now, we can subtract the two fractions.
3/6 - 2/6 = 1/6
So, there is a 1/6 probability of drawing a yellow marble.