Question

A box has 1 red marble, 3 blue marbles, and 4 green marbles. Maya draws a blue marble randomly from the box, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row? Explain your answer.

Answer 1

Answer:

$\dfrac{9}{64}$

Step-by-step explanation:

Sampling with replacement means that we choose a marble, note its colour, put it back and shake the box, then choose a marble again.

There are $1+3+4=8$ marbles in total. The probability that the first chosen marble is blue is $\dfrac{3}{8}.$ then Maya replaces this marble and the probability of choosing the second blue marble is the same. Using the product rule, the probability of drawing 2 blue marbles in a row is

$\dfrac{3}{8}\cdot \dfrac{3}{8}=\dfrac{9}{64}.$