On the second day of Statistics, my teacher gave to me….two turtle doves. The pet store that my Statistics teacher frequents has 25 doves, of which 8 are turtle doves. (See * below. This is not a trick question as turtle doves really do exist. If you are visualizing a cross between a turtle and a dove, forget the idea. Turtle cheesecake does not contain any turtle either, and I can assure you that it exists also) What is the probability that the Statistics teacher randomly selected two turtle doves from this pet store?

Question

On the second day of Statistics, my  teacher gave to me….two turtle doves.    The pet store that my Statistics teacher frequents has 25 doves, of which 8 are turtle doves.  (See  * below.  This is not a trick question as  turtle doves really do exist.  If you are visualizing a cross between a turtle and a dove, forget the idea.  Turtle cheesecake does not contain any turtle either, and I can assure you that it exists also)   What is the probability that the Statistics teacher randomly selected two turtle doves from this pet store?

Steve · Answer

This just like drawing without replacement, so your probability is 8/25 * 7/24 = 7/75

Explain Bot · Answer

To find the probability of randomly selecting two turtle doves from the pet store, we need to consider the total number of possible outcomes and the number of favorable outcomes. The total number of possible outcomes is the total number of ways to select two doves from the 25 available doves in the pet store. This can be calculated using combinations. The formula for combinations is given by: C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being selected. In this case, n = 25 (total number of doves in the pet store) and r = 2 (number of turtle doves we want to select). Using the formula, we can calculate the total number of possible outcomes: C(25, 2) = 25! / (2!(25-2)!) = 25! / (2! * 23!) = (25 * 24) / (2 * 1) = 300. So, there are 300 possible ways to select two doves from the pet store. The number of favorable outcomes is the number of ways to select 2 turtle doves from the 8 available turtle doves in the pet store. Again, we can use combinations to find this: C(8, 2) = 8! / (2!(8-2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28. So, there are 28 favorable outcomes where we select two turtle doves. Now, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes: Probability = favorable outcomes / total outcomes = 28 / 300 ≈ 0.0933 (rounded to four decimal places). Therefore, the probability that the Statistics teacher randomly selected two turtle doves from the pet store is approximately 0.0933 or 9.33%.