On the fifth day of Statistics, my teacher gave to me….five golden rings. The rings from which she could select were: 10 golden rings, 5 silver rings and 3 platinum rings. Knowing that your Statistics teacher would naturally have randomly selected the rings, what is the probability that the first two rings she randomly selects would be pure gold rings?

18 rings total, so that would make the probability

10/18 * 9/17

so it would be 90/306 which would be simplified to 5/17

To calculate the probability of selecting two pure gold rings, we need to know the total number of rings and the number of pure gold rings available.

In this case, the total number of rings is the sum of the golden rings, silver rings, and platinum rings, which is 10 + 5 + 3 = 18.

The number of pure gold rings available is 10.

Now, we can calculate the probability of selecting two pure gold rings by dividing the number of ways to select two pure gold rings by the total number of possible selections.

The number of ways to select two pure gold rings can be calculated using combinations. We can think of this as choosing 2 objects out of the 10 pure gold rings. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of objects and r is the number of objects to be chosen.

In this case, C(10, 2) = 10! / (2! * (10 - 2)!) = 45.

The total number of possible selections of two rings from the 18 available rings can be calculated using combinations as well. We can think of this as choosing 2 objects out of the 18 rings. The formula for combinations is the same as before.

C(18, 2) = 18! / (2! * (18 - 2)!) = 153.

Finally, the probability can be calculated by dividing the number of ways to select two pure gold rings by the total number of possible selections:

Probability = number of ways to select two pure gold rings / total number of possible selections
= 45/153
= 0.2941 (rounded to four decimal places) or approximately 29.41%.

Therefore, the probability that the first two rings she randomly selects would be pure gold rings is 0.2941 or approximately 29.41%.