Final answer:
The probability of drawing two red marbles consecutively from a bag without replacement is 0.143, when calculated by multiplying the probability of drawing the first red marble (6/15) with the probability of drawing a second red marble after the first one has been drawn (5/14).
Step-by-step explanation:
The student's question pertains to the probability of drawing two red marbles consecutively from a bag without replacement. The bag initially contains 6 red marbles, 4 blue marbles, and 5 green marbles, making a total of 15 marbles. To calculate this probability, we use the formula for conditional probability since the second draw depends on the outcome of the first.
The probability of drawing the first red marble is 6/15 (since there are 6 red marbles out of 15). Upon drawing one red marble, there are now 5 red marbles left and a total of 14 marbles. The probability of drawing a second red marble is then 5/14. Multiply these probabilities together to get the probability of both events happening in sequence:
Probability of 1st red: 6/15
Probability of 2nd red after 1st red: 5/14
Total probability: (6/15) × (5/14) = 30/210 = 1/7 ≈ 0.143
To the nearest thousandth, this probability is 0.143.