Probability Question....Midterm preparation... I'm a little lost.....?

Question

I have a my calculus midterm tomorrow. I am not sure if I am answering this question correctly. Please help.

Question: An urn contains 18 black marbles and 32 white marbles, and 8 marbles are selected from the urn WITH replacement, and independently of each other.

What is the probability that the exactly 4 of the marbles are black, given that the first marble selected is black?

Here, I am debating whether it is 8C3 ( or 17C3- because one is removed, but then it is with replacement) times 32C4 all over 50 ^8.

I am in a dilemma. Please help with any input. I need to understand what I am doing wrong. Thank you for any input.

Answer 1

This sounds like a probability class, not calculus.

Question: An urn contains 18 black marbles and 32 white marbles, and 8 marbles are selected from the urn WITH replacement, and independently of each other.

What is the probability that the exactly 4 of the marbles are black, given that the first marble selected is black?
______

The probability for drawing one white or one black marble is shown below.

P(W) = 32/(18 + 32) = 32/50 = 16/25
P(B) = 18/(18 + 32) = 18/50 = 9/25

These probabilities will remain unchanged for each marble drawn because they are drawn with replacement. Since it is given that the first marble drawn is black, the problem reduces to drawing exactly 3 black marbles out of 7.

P(3B | 7 drawn) = (7C3)* [(9/25)^3] * [(16/25)^4]

Answer 2

With replacement and independently are the key words. The probability of drawing a black marble is the same each time: 18/50 = 9/25.

Okay, you are given that the first marble is black, meaning exactly three of the remaining seven ought to be black.

7 C 3 ways to order the black and whites, for example:
B B B W W W W
B B W W W W B
etc, etc

Then, three need to be black, so the term (9/25)^3 should be there. Four need to be not black (white), so the term (16/25)^4 should be there.

The answer:
(7 C 3) * (9/25)^3 * (16/25)^4

This problem is in a calculus class? Really?

Answer 3

Here you have to consider the concept of conditional probability.

Answer 4

i think it should be 8C3.i cant give explanation for this question in typing.sorry