Question
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.
Answers
GPT 3.5
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.
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.