A box has 1 red marble, 3 blue marbles, and 4 green marbles. Maya draws a marble randomly from the box, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles? Explain your answer.
First, we need to find the probability of drawing a blue marble on the first draw. There are a total of 8 marbles in the box, and 3 of them are blue. So, the probability of drawing a blue marble on the first draw is 3/8.
Since the marble is replaced after the first draw, the total number of marbles in the box remains the same for the second draw. Therefore, the probability of drawing a blue marble on the second draw is also 3/8.
To find the probability of drawing 2 blue marbles, we multiply the probabilities of each event happening:
P(2 blue marbles) = P(blue on first draw) * P(blue on second draw)
P(2 blue marbles) = (3/8) * (3/8)
P(2 blue marbles) = 9/64
Therefore, the probability of drawing 2 blue marbles in succession is 9/64 or approximately 0.1406.