Question

1. milo has a bag of marbles. there are 5 green, 4 blue, 6 orange, and 3 red. what is the probability that milo will select a blue marble and then a red marble without replacing the first marble? 1/27 1/21 9/34 2/51

Explanation:

Step1: Calculate total marbles

First, find the total number of marbles. Add the number of each color: \(5 + 4 + 6 + 3 = 18\) marbles in total.

Step2: Probability of blue first

The probability of selecting a blue marble first is the number of blue marbles divided by total marbles: \(\frac{4}{18}=\frac{2}{9}\).

Step3: Probability of red after blue

After removing one blue marble, the total number of marbles becomes \(18 - 1 = 17\). The number of red marbles is 3, so the probability of selecting a red marble next is \(\frac{3}{17}\).

Step4: Multiply the probabilities

To find the probability of both events happening (blue then red without replacement), multiply the two probabilities: \(\frac{2}{9}\times\frac{3}{17}=\frac{6}{153}=\frac{2}{51}\).

Answer:

\(\frac{2}{51}\) (corresponding to the option with \(2/51\))