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)(3/6) = 1/27
To find the probability of drawing a red marble three times, we need to calculate the probability of drawing a red marble on each individual draw and then multiply those probabilities together.
Given that there are 3 red marbles and 6 green marbles, the probability of drawing a red marble on the first draw is:
P(Red on 1st draw) = Number of red marbles / Total number of marbles
= 3 / (3 + 6)
= 3 / 9
= 1/3
Since we are replacing the marble after each draw, the probability remains the same for subsequent draws.
Therefore, the probability of drawing a red marble on the second draw is also 1/3:
P(Red on 2nd draw) = 1/3
Similarly, the probability of drawing a red marble on the third draw is also 1/3:
P(Red on 3rd draw) = 1/3
To find the probability of all three events occurring, we multiply the individual probabilities together:
P(Red on 1st, 2nd, 3rd draw) = P(Red on 1st draw) × P(Red on 2nd draw) × P(Red on 3rd draw)
= (1/3) × (1/3) × (1/3)
= 1/27
Therefore, the probability of drawing a red marble all three times is 1/27.