Final answer:
The probability of picking a blue marble both times without replacement from a bag containing 3 blue and 5 red marbles is 3/28, which is calculated by multiplying 3/8 (probability of first blue) by 2/7 (probability of second blue given first was blue).
Step-by-step explanation:
To find the probability of picking a blue marble both times from a bag containing 3 blue and 5 red marbles, we calculate the probability of each event occurring consecutively without replacement. There are a total of 3 + 5 = 8 marbles initially.
The probability of picking a blue marble on the first try is the number of blue marbles divided by the total number of marbles, so P(blue first) = 3/8.
When a blue marble is taken out and not replaced, there are now 2 blue marbles and 5 red marbles left, making 7 marbles in total. The probability of picking another blue marble is now P(blue second | blue first) = 2/7.
To find the overall probability of both events happening, we multiply the individual probabilities of each event occurring:
P(blue first and blue second) = P(blue first) × P(blue second | blue first) = (3/8) × (2/7) = 6/56 = 3/28.
Therefore, the correct answer is B. 3/28.