Bag A contains 3 white marbles and 2 red marbles. Bag B contains 6 white marbles and 3 red marbles, find the probability of drawing a white marble from Bag A followed by a white marble from Bag B.
A = 3/5, B = 6/9
The probability of all events occurring is found by multiplying the probabilities of the individual events.
1/5
1/8
To find the probability of drawing a white marble from Bag A followed by a white marble from Bag B, we need to calculate the individual probabilities and then multiply them together.
Probability of drawing a white marble from Bag A:
Bag A contains 3 white marbles and 2 red marbles, so the total number of marbles is 3 + 2 = 5.
The probability of drawing a white marble from Bag A is given by:
P(white from A) = (number of white marbles in Bag A) / (total number of marbles in Bag A)
P(white from A) = 3 / 5
Probability of drawing a white marble from Bag B:
Bag B contains 6 white marbles and 3 red marbles, so the total number of marbles is 6 + 3 = 9.
The probability of drawing a white marble from Bag B is given by:
P(white from B) = (number of white marbles in Bag B) / (total number of marbles in Bag B)
P(white from B) = 6 / 9
Now, to find the overall probability of drawing a white marble from Bag A followed by a white marble from Bag B, we multiply the two probabilities together:
P(white from A and then white from B) = P(white from A) * P(white from B)
P(white from A and then white from B) = (3 / 5) * (6 / 9)
Calculating this expression, we get:
P(white from A and then white from B) = 18 / 45
Simplifying the fraction, we can divide the numerator and denominator by their greatest common divisor, which in this case is 9:
P(white from A and then white from B) = 2 / 5
Therefore, the probability of drawing a white marble from Bag A and then a white marble from Bag B is 2/5.