A box contains ten marbles,seven of which are black and three are red.three marbles are drawn one after the other without replacement.finf the probability of choosing

One red,one black and one red marble(in that order)
At least two marbles
At least two black marbles
At most two black marbles

P(r,b,r) = 3/10 * 7/9 * 2/8

since you are drawing 3 marbles, I'd say that P(at least 2) = 1
P(<2b) = P(0b) + P(1b) = (3/10 * 2/9 * 1/8) + 3*(7/10 * 3/9 * 2/8)
P(≤2b) = P(<2b) + P(2b) = P(<2b) + 3(7/10 * 6/9 * 3/8)
P(≥2b) = 1 - P(<2b)

I had a long answer typed out, but realized you need to multiply combinations after subtracting from the numerator or denominator. Crap. Anyways, good luck! I need to stop lurking and return to my own work. :)

To find the probability of each event, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

1. Probability of choosing one red, one black, and one red marble (in that order):
Total number of possible outcomes = Total number of marbles = 10
Number of favorable outcomes:
- First pick a red marble: 3/10
- On the second pick, choose a black marble (since we already picked a red one): 7/9
- Finally, pick another red marble: 2/8
Therefore, the probability is (3/10) * (7/9) * (2/8) = 7/120 = 7/120.

2. Probability of choosing at least two marbles:
We can calculate this probability by finding the probability of choosing no marbles and subtracting it from one.
The probability of choosing no marbles is the same as the probability of choosing three marbles of the same color: either all black or all red.
Number of ways to choose all black = 7/10 * 6/9 * 5/8 = 7/24
Number of ways to choose all red = 3/10 * 2/9 * 1/8 = 1/120
Probability of choosing no marbles = (7/24) + (1/120) = 31/120
Probability of choosing at least two marbles = 1 - 31/120 = 89/120.

3. Probability of choosing at least two black marbles:
We can calculate this probability by finding the probability of choosing no black marbles and subtracting it from one.
The probability of choosing no black marbles is the same as the probability of choosing three red marbles.
Number of ways to choose three red marbles = 3/10 * 2/9 * 1/8 = 1/120
Probability of choosing no black marbles = 1/120
Probability of choosing at least two black marbles = 1 - 1/120 = 119/120.

4. Probability of choosing at most two black marbles:
We can calculate this probability by finding the probability of choosing no black marbles.
The probability of choosing no black marbles is the same as the probability of choosing three red marbles.
Probability of choosing no black marbles = 3/10 * 2/9 * 1/8 = 1/120.
Therefore, the probability of choosing at most two black marbles is 1 - 1/120 = 119/120.

I hope this explanation helps you understand how to calculate these probabilities.