A bag contains 4 red and 3 green blocks. 3 blocks are randomly selected from the bag. Determine the probability that all three are red given that

i.) replacement occurs between the second and third selections

ii.) no replacement occurs

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- Jul 10th 2007, 05:03 PMsam48probability using permutations/combinations
A bag contains 4 red and 3 green blocks. 3 blocks are randomly selected from the bag. Determine the probability that all three are red given that

i.) replacement occurs between the second and third selections

ii.) no replacement occurs - Jul 10th 2007, 05:59 PMSoroban
Hello, Sam!

Quote:

A bag contains 4 red and 3 green blocks.

Three blocks are randomly selected from the bag.

Determine the probability that all three are red given that:

a) replacement occurs between the second and third selections

Second block is red: $\displaystyle P(\text{\#2 red}) = \frac{3}{6}$ . . . . The second block replaced.

Third block is red: $\displaystyle P(\text{\#3 red}) = \frac{3}{6}$

Therefore: $\displaystyle P(\text{3 red}) \;=\;\frac{4}{7}\cdot\frac{3}{6}\cdot\frac{3}{6} \;=\;\frac{1}{7}$

Quote:

b) no replacement occurs

Second block is red: $\displaystyle P(\text{\#2 red}) = \frac{3}{6}$

Third block is red: $\displaystyle P(\text{\#3 red}) = \frac{2}{5}$

Therefore: $\displaystyle P(\text{3 red}) \;=\;\frac{4}{7}\cdot\frac{3}{6}\cdot\frac{2}{5} \;=\;\frac{4}{35}$