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
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
Hello, Sam!
First block is red: $\displaystyle P(\text{\#1 red}) = \frac{4}{7}$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: $\displaystyle P(\text{3 red}) \;=\;\frac{4}{7}\cdot\frac{3}{6}\cdot\frac{3}{6} \;=\;\frac{1}{7}$
First block is red: $\displaystyle P(\text{\#1 red}) = \frac{4}{7}$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: $\displaystyle P(\text{3 red}) \;=\;\frac{4}{7}\cdot\frac{3}{6}\cdot\frac{2}{5} \;=\;\frac{4}{35}$