Question

all of the marbles in a bag are the same size and shape.
color number
yellow 10
blue 13
red 5
green 18

• kendra randomly selects a marble from the bag, replaces it, and then randomly selects a second marble.
• andie randomly selects a marble from the bag, does not replace it, and then randomly selects a second marble.

who has the least probability of selecting a green marble followed by a yellow marble?
kendra
andie
none of the above

Explanation:

Step1: Calculate total number of marbles

$10 + 13+5 + 18=46$

Step2: Calculate Kendra's probability

Since it's with - replacement, the probability of first green and then yellow is $P_{Kendra}=\frac{18}{46}\times\frac{10}{46}=\frac{180}{2116}$

Step3: Calculate Andie's probability

Since it's without - replacement, the probability of first green and then yellow is $P_{Andie}=\frac{18}{46}\times\frac{10}{45}=\frac{180}{2070}$

Step4: Compare the probabilities

Since $\frac{180}{2116}<\frac{180}{2070}$, Kendra has the least probability.

Answer:

Kendra