A jar contains 7 yellow balls, and 8 green balls. two balls are drawn randomly, one after the other, without replacement, what is the probability that the first ball is green and the second ball is yellow?

We can calculate the probability that the first ball is green and the second ball is yellow by breaking it down step by step.

### Step 1: Probability that the first ball is green.
- There are 8 green balls out of a total of 15 balls (7 yellow + 8 green).
- The probability of drawing a green ball first is:
\[
P(\text{first green}) = \frac{8}{15}
\]

### Step 2: Probability that the second ball is yellow after drawing a green ball first.
- After one green ball is drawn, there are 7 yellow balls left out of 14 remaining balls (since one green ball has already been removed).
- The probability of drawing a yellow ball second is:
\[
P(\text{second yellow | first green}) = \frac{7}{14} = \frac{1}{2}
\]

### Step 3: Multiply the probabilities.
The probability of both events happening (first drawing a green ball and then drawing a yellow ball) is the product of these two probabilities:
\[
P(\text{green, then yellow}) = P(\text{first green}) \times P(\text{second yellow | first green}) = \frac{8}{15} \times \frac{1}{2} = \frac{8}{30} = \frac{4}{15}
\]

Thus, the probability of drawing a green ball first and a yellow ball second is:
\[
\boxed{\frac{4}{15}}
\]

Would you like a detailed breakdown of these steps or have any further questions?

### Related Questions:
1. What is the probability of drawing two green balls consecutively?
2. What is the probability of drawing two yellow balls consecutively?
3. What is the probability that the first ball is yellow and the second is green?
4. How does the probability change if the balls are replaced after each draw?
5. What is the probability of drawing two balls of the same color in a row?

### Tip:
When calculating probabilities without replacement, the total number of items decreases after each draw. Always adjust the denominator accordingly.

A jar contains 7 yellow balls, and 8 green balls. Two balls are drawn randomly, one after the other, without replacement. What is the probability that the first ball is green and the second ball is yellow?

Learn how to calculate the probability of drawing a green ball first and a yellow ball second from a jar containing 7 yellow balls and 8 green balls, without replacement. This problem covers key probability concepts, including conditional probability and combinatorics. Suitable for students in Grades 6-8.

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