Question

A bag contains 4 red marbles and 2 white marbles. A marble is selected, kept out of the bag, and then another marble is selected. What is P(red, then white)?

A) 2/5
B) 4/15
C) 1/3
D) 2/9

Answer 1

To calculate the probability of drawing a red and then a white marble from the bag without replacement, multiply the probability of each event occurring sequentially. The probability is 1/3.

Step-by-step explanation:

The student is asking about the probability of drawing a red marble and then a white marble from a bag that contains a mix of red and white marbles. This type of problem is solved using the concepts of probability without replacement. Since there are initially 4 red marbles and 2 white marbles, the probability of drawing a red marble first is ¼ (since there are 4 red out of 6 total marbles).

After a red marble is drawn and kept aside, there are now 3 red marbles and 2 white marbles left in the bag, making a total of 5 marbles. The probability of then drawing a white marble is ½ (since there are 2 white out of 5 marbles left). To find the combined probability of both events happening in sequence (drawing a red and then a white marble), we multiply the probabilities of the individual events: ½ * ½ = ⅓.

Therefore, the correct answer is C) 1/3, which is the probability of drawing a red marble followed by a white marble when one marble is drawn and kept out of the bag before drawing the second marble.