Question

Consider a bag with marbles: 3 blue marbles, 4 red marbles, and 8 green marbles. Two marbles are drawn in sequence and taken without replacement. What is the probability of drawing a red marble first and then a green marble?

Answer 1

The probability of drawing a red marble first and then a green marble is 7/18.

Step-by-step explanation:

The probability of drawing a red marble first and then a green marble can be calculated using the concept of conditional probability. Let's break down the steps:

1. Calculate the probability of drawing a red marble first. There are a total of 9 marbles in the bag, so the probability of drawing a red marble first is 4/9.
2. Once the first marble is drawn, there will be a total of 8 marbles left in the bag, with 7 of them being green. So, the probability of drawing a green marble after drawing a red marble is 7/8.
3. To find the overall probability, multiply the probabilities of drawing a red marble first and then a green marble: (4/9) * (7/8) = 28/72, which simplifies to 7/18.

Therefore, the probability of drawing a red marble first and then a green marble is 7/18.