An urn contains 6 red balls and 9 green balls two balls are drawn in succession wihout replacement what is the probability that first is red and second is green .

Answer

To solve the problem of finding the probability that the first ball drawn is red and the second ball drawn is green, we can follow these steps:

### Step 1: Determine the total number of balls in the urn.
- The urn contains 6 red balls and 9 green balls.
- Total number of balls = 6 (red) + 9 (green) = 15 balls.

**Hint:** Always start by calculating the total number of items in the scenario.

### Step 2: Calculate the probability of drawing a red ball first.
- The probability of drawing a red ball first (P(Red)) is the number of red balls divided by the total number of balls.
- P(Red) = Number of red balls / Total number of balls = 6 / 15 = 2 / 5.

**Hint:** Use the formula for probability: P(Event) = Number of favorable outcomes / Total outcomes.

### Step 3: Calculate the probability of drawing a green ball second, given that the first ball drawn was red.
- After drawing one red ball, there are now 5 red balls and 9 green balls left in the urn.
- Total balls left = 5 (red) + 9 (green) = 14 balls.
- The probability of drawing a green ball second (P(Green | Red)) is the number of green balls left divided by the total number of balls left.
- P(Green | Red) = Number of green balls / Total number of balls left = 9 / 14.

**Hint:** Remember that the total number of balls changes after the first draw, which affects the probability of the second draw.

### Step 4: Calculate the combined probability of both events.
- The combined probability of both events happening (first red and then green) is found by multiplying the probabilities of the two independent events.
- P(Red and then Green) = P(Red) * P(Green | Red) = (2/5) * (9/14).

**Hint:** When calculating the probability of two dependent events, multiply their individual probabilities.

### Step 5: Simplify the final probability.
- P(Red and then Green) = (2/5) * (9/14) = 18 / 70.
- Simplifying 18 / 70 gives us 9 / 35.

**Hint:** Always simplify your final answer to its lowest terms for clarity.

### Final Answer:
The probability that the first ball drawn is red and the second ball drawn is green is **9/35**.

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