A bag contains 11 red marbles and 4 green marbles.  what are the odds of a red marble first then a red marble second without replacing

To find the probability of drawing two red marbles in succession without replacement from a bag containing 11 red marbles and 4 green marbles (15 marbles total), we proceed step by step:

### Step 1: Probability of drawing a red marble first
- There are 11 red marbles out of 15 total marbles.
- So, the probability of drawing a red marble first is:
  \[
  P(\text{Red 1st}) = \frac{11}{15}
  \]

### Step 2: Probability of drawing a red marble second without replacement
- After drawing one red marble, there are now 10 red marbles left, and only 14 total marbles remain.
- So, the probability of drawing a second red marble is:
  \[
  P(\text{Red 2nd | Red 1st}) = \frac{10}{14}
  \]

### Step 3: Multiply the probabilities
The overall probability of drawing two red marbles in a row without replacement is:
\[
P(\text{Red 1st and Red 2nd}) = \frac{11}{15} \times \frac{10}{14}
\]
\[
P(\text{Red 1st and Red 2nd}) = \frac{110}{210} = \frac{11}{21}
\]

Thus, the probability of drawing two red marbles in succession without replacement is \( \frac{11}{21} \).

Would you like further details or any additional questions?

Here are 5 related questions for further practice:
1. What is the probability of drawing two green marbles in a row without replacement?
2. What are the odds of drawing a red marble first and a green marble second without replacement?
3. If one marble is drawn and replaced, what are the odds of drawing two red marbles in a row?
4. How does the probability change if there are 6 green and 9 red marbles?
5. What is the probability of drawing one red and one green marble in any order without replacement?

**Tip:** When calculating probabilities without replacement, remember that the total number of items decreases after each draw.

A bag contains 11 red marbles and 4 green marbles. What are the odds of a red marble first then a red marble second without replacing?

Explore how to calculate the probability of drawing two red marbles in a row from a bag containing 11 red and 4 green marbles, without replacement. This step-by-step solution uses probability rules for dependent events. Suitable for students in Grades 6-8.

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