# A bag contains 8 blue and 4 yellow balls. Two balls are taken randomly at a time from the bag. Find the probability that both balls are yellow? Without replacement: With replacement:

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With replacement = 1:9

Without replacement = 1:11

#### Explanation:

**With replacement:**

Each time we take out a ball, the number of balls in the bag **stays the same**.

This means that we will always have 12 balls in the bag, and there will always be 4 yellow, and 8 blue.

Knowing this, every time we have a **1 in 3** chance of pulling a yellow ball.

Since we are trying to pull **2** yellow balls, the probability of doing so is:

**Without replacement**

Each time we take out a ball, the number of balls in the bag **decreases by one**.

This means that after the first yellow ball is pulled, there will only be 11 balls in the bag, and only 3 yellow balls remain.

The probability of pulling a yellow ball is equal to the number of yellow balls divided by the total number of balls in the bag.

The probability of pulling **2** yellow balls is:

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Describe your changes (optional) 200

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Without replacement:

With replacement:

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To have BOTH balls yellow means we want to find:

For the first ball:

If the ball is **NOT replaced**, there is one less yellow ball and one less ball.

For the second ball:

If the first ball **IS replaced**, the probability stays the same for the second ball being yellow.

For the second ball:

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Describe your changes (optional) 200

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#### Explanation:

1) without replacement:

2) with replacement:

Explanation :

.

If the ball is replaced, the second time we have the same probability

However if the ball is not replaced, there are only

Describe your changes (optional) 200