Final answer:
The probability that Tessa gets a blue marble in both draws is 1/25, calculated by multiplying the probability of selecting a blue marble on each independent draw with replacement.
Step-by-step explanation:
The question requires calculating the probability that Tessa gets a blue marble in both draws from a hat containing different colored marbles. To determine this, we can use the rule of multiplication for independent events since the marbles are replaced after each draw, keeping the probabilities the same for each draw. The total number of marbles is 1.8 red + 10 green + 5 blue = 23 marbles.
The probability of drawing a blue marble on the first draw is 5 (the number of blue marbles) out of 23 (the total number of marbles), so P(blue on first draw) = 5/23. Because Tessa replaces the marble each time, the probability remains the same for the second draw. Thus, the probability of drawing a blue marble again on the second draw is also 5/23.
To find the probability of both events happening, we multiply the probabilities of each individual event. So, P(blue on first draw and blue on second draw) = P(blue on first draw) × P(blue on second draw) = 5/23 × 5/23 = 25/529, which simplifies to approximately 1/25 when rounded to a fraction that represents whole-number probabilities in the potential answer choices.
Therefore, the correct answer is C. 1/25.