a box contains 3 red marbles, 4 white marbles and 5 yellow marbles.find the probability that a red marble and then a yellow marble to be pick up on two successives drawing then there is a replacement of the marbles
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
If replacement, then:
3/12 * 5/12 = ?
To find the probability of drawing a red marble and then a yellow marble with replacement, you need to calculate the probability of each event and multiply them together.
The probability of drawing a red marble on the first draw is the number of red marbles divided by the total number of marbles:
P(Red on first draw) = 3 / (3 + 4 + 5) = 3 / 12 = 1 / 4
Since there is replacement (putting the drawn marble back into the box), the total number of marbles remains the same for the second draw.
The probability of drawing a yellow marble on the second draw is the number of yellow marbles divided by the total number of marbles:
P(Yellow on second draw) = 5 / (3 + 4 + 5) = 5 / 12
To find the probability of both events happening, you multiply the probabilities together:
P(Red and then Yellow) = P(Red on first draw) x P(Yellow on second draw)
= (1 / 4) x (5 / 12)
= 5 / 48
Therefore, the probability of drawing a red marble and then a yellow marble with replacement is 5/48.