# Math Help - probability using permutations/combinations

1. ## probability 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

2. Hello, Sam!

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
First block is red: $P(\text{\#1 red}) = \frac{4}{7}$
Second block is red: $P(\text{\#2 red}) = \frac{3}{6}$ . . . . The second block replaced.
Third block is red: $P(\text{\#3 red}) = \frac{3}{6}$

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

b) no replacement occurs
First block is red: $P(\text{\#1 red}) = \frac{4}{7}$
Second block is red: $P(\text{\#2 red}) = \frac{3}{6}$
Third block is red: $P(\text{\#3 red}) = \frac{2}{5}$

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