Suppose you have a jar with 20 marbles. 12 marbles are red, and 8 marbles are blue. You draw marbles one at a time from the jar, without replacing them. What is the probability of drawing a blue marble, then a blue marble, then a red marble? Round your answer to at least 4 decimals. Question Help: Video

Step 1 ：Let's start with a jar containing 20 marbles, 12 of which are red and 8 are blue.

Step 2 ：We are drawing marbles one at a time from the jar, without replacing them. We want to find the probability of drawing a blue marble, then another blue marble, and finally a red marble.

Step 3 ：The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, we need to calculate the probability of three independent events happening in sequence. The probability of each event changes after each draw because the marbles are not replaced.

Step 4 ：The probability of drawing a blue marble on the first draw is the number of blue marbles divided by the total number of marbles, which is \(\frac{8}{20} = 0.4\).

Step 5 ：After a blue marble is drawn, the probability of drawing a blue marble on the second draw is the number of remaining blue marbles divided by the remaining total number of marbles, which is \(\frac{7}{19} = 0.3684210526315789\).

Step 6 ：Similarly, the probability of drawing a red marble on the third draw is the number of red marbles divided by the remaining total number of marbles, which is \(\frac{12}{18} = 0.6666666666666666\).

Step 7 ：The probability of all three events happening in sequence is the product of their individual probabilities, which is \(0.4 \times 0.3684210526315789 \times 0.6666666666666666 = 0.0982456140350877\).

Step 8 ：So, the probability of drawing a blue marble, then a blue marble, then a red marble is approximately 0.0982.

Step 9 ：Final Answer: \(\boxed{0.0982}\)