a box contains 100 marbles. Five of the marbles are purple and the rest are green. if eight marbles are drawn without replacement ,what is the probability of obtaining exactly two purple marbles?

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

5/100 * 4/99 * 95/98 * 94/97 * 93/96 * 92/95 * 91/94 * 90/93 = ?

Or you could explore combinations and permutations.

https://www.mathsisfun.com/combinatorics/combinations-permutations.html

To find the probability of obtaining exactly two purple marbles, we need to calculate two things: the number of total possible outcomes and the number of favorable outcomes.

First, let's calculate the number of total possible outcomes. Since there are 100 marbles in total, and we are drawing 8 marbles without replacement, the number of total possible outcomes can be calculated using the combination formula, also known as "n choose r" or "nCr". The formula is:

nCr = n! / (r! * (n-r)!)

where "n" is the total number of items and "r" is the number of items chosen.

In this case, since we are drawing 8 marbles out of 100, we can calculate:

nCr = 100! / (8! * (100-8)!)

Calculating this gives us the total number of possible outcomes.

Next, let's calculate the number of favorable outcomes, which is the number of ways to draw exactly two purple marbles.

Since there are 5 purple marbles in the box, we need to choose 2 of them. This can be calculated using the combination formula as well:

nCr = 5! / (2! * (5-2)!)

Calculating this gives us the number of favorable outcomes.

Finally, we can find the probability by dividing the number of favorable outcomes by the number of total possible outcomes:

Probability = Number of Favorable Outcomes / Number of Total Possible Outcomes

Now, you can substitute the values and calculate the probability of obtaining exactly two purple marbles.