A bag contains 16 congruent blocks, 4 of which are blue and 12 of which are red. Two blocks are randomly pulled from the bag at the same time. What is the probability that both blocks are blue? Express your answer as a common fraction.

Glowlife Jan 20, 2022

#1**+1 **

Because both blocks are pulled at the same time, there is a \({1 \over 4} * {3 \over 16} = {3 \over 64}\) chance that both balls will be blue. Correct me if I am wrong.

BuilderBoi Jan 20, 2022

#2**+1 **

*A bag contains 16 congruent blocks, 4 of which are blue and 12 of which are red. Two blocks are randomly pulled from the bag at the same time. What is the probability that both blocks are blue? Express your answer as a common fraction.*

Arbitrarily call either block the first one.

The chance that the first block is blue is 4 / 16.

For both blocks to be blue, the first one had to be blue.

Therefore, 3 of the remaining 15 blocks are blue.

The chance that the second block is blue is 3 / 15.

For both things to happen, multiply their chances.

( 4 / 16 ) • ( 3 / 15 ) = 12 / 240 => this reduces to **1 / 20**.

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Guest Jan 20, 2022