a bag contains 3 red marbles and 6 green marbles a marble is drawn and then replaced a second marble is drawn and replaced and then a third marble is drawn . What is the probability that a red marble is drawn all 3 times?
3/9 * 3/9 * 3/9
What is the probability of selecting a purple marble and then a white marble?
What is the probability of selecting two white marbles?
Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work.
What is the probability of selecting a purple marble and then a white marble?
What is the probability of selecting two white marbles?
Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work.
To find the probability of drawing a red marble all three times, we need to determine the probability of drawing a red marble on each individual draw and then multiply them together.
The probability of drawing a red marble on the first draw is the number of red marbles in the bag divided by the total number of marbles:
P(Red on 1st draw) = Number of red marbles / Total number of marbles
= 3 / (3 + 6) (since there are 3 red marbles and a total of 9 marbles)
= 3/9
= 1/3
Since we replace each marble after drawing it, the probabilities remain the same for each draw. Therefore, the probability of drawing a red marble on the second and third draws are also 1/3 each.
To find the probability of all three events happening, we can multiply the probabilities together:
P(Red on 1st, 2nd, and 3rd draws) = P(Red on 1st draw) * P(Red on 2nd draw) * P(Red on 3rd draw)
= (1/3) * (1/3) * (1/3)
= 1/27
So, the probability of drawing a red marble all three times is 1/27.