Question

In a bag, there are 4 blue marbles, 8 red marbles, 5 yellow marbles, and 1 green marble. With replacement, what is the probability of selecting a green marble and then a yellow marble?

1) 1/90
2) 1/18
3) 1/20
4) 1/10

Answer 1

The probability of selecting a green marble followed by a yellow marble with replacement from the bag is 5/324. Since this doesn't match any of the provided options, the student should recheck the question and options.

Step-by-step explanation:

The question involves calculating the probability of selecting a green marble followed by a yellow marble from a bag with multiple marbles of different colors, with replacement. The answer involves multiplying the individual probabilities of selecting each marble. For the first event, the probability of choosing a green marble is 1 out of the total number of marbles; for the second event, the probability of selecting a yellow marble also depends on the total number of marbles in the bag.

Let's calculate the probabilities step by step:

1. Determine the total number of marbles in the bag:
   4 (blue) + 8 (red) + 5 (yellow) + 1 (green) = 18 marbles total.
2. Calculate the individual probabilities:
   Probability of selecting a green marble (P(Green)) = 1/18.
   Since we are replacing the marble, the total number of marbles remains the same for the second draw. Probability of selecting a yellow marble (P(Yellow)) = 5/18.
3. Multiply the individual probabilities to get the combined probability:
   P(Green then Yellow) = P(Green) x P(Yellow) = (1/18) x (5/18) = 5/324.

However, none of the provided options match the correct answer (5/324). Therefore, the student should be advised to check the question and the options provided again.