A biologist must select 4 fishes from a pond with a population of 100. The probability of selecting the four fishes is?
The probability of selecting the four fishes is 1 in 15,625 (1/15625).
Well, selecting fish from a pond can be quite a fin-tastic experience! To calculate the probability of selecting four fishes from a population of 100, we need to use a little math.
The probability of selecting the first fish is 4 out of 100, which can also be written as 4/100 or 1/25. After selecting the first fish, the probability of selecting the second fish decreases to 3 out of 99 or 3/99.
Continuing this pattern, the probability of selecting the third fish would be 2/98, and the probability of selecting the fourth fish would be 1/97.
To find the overall probability, simply multiply the individual probabilities together:
(1/25) * (3/99) * (2/98) * (1/97) = 1/365850
So, the probability of selecting those four fishes from the pond is approximately 1 in 365,850. That's quite a reel-y low probability! Happy fishing! 🐟🎣
To calculate the probability of selecting four fishes from a pond with a population of 100, we need to determine the total number of ways to select four fishes from a population of 100.
Since the order in which the fishes are selected does not matter in this case (it is assumed that all fishes are identical), we can use the combination formula.
The combination formula is given by:
nCr = n! / (r! * (n - r)!)
Where n is the total number of items available (population), and r is the number of items to be selected.
In this case, n = 100 (population) and r = 4 (number of fishes to be selected).
Plugging in the values:
nCr = 100! / (4! * (100 - 4)!)
Simplifying this expression:
nCr = 100! / (4! * 96!)
Now, we can calculate the factorial of 100:
100! = 100 * 99 * 98 * ... * 3 * 2 * 1
And similarly, we can calculate the factorials of 4 and 96.
Finally, we can substitute these values back into the combination formula and evaluate the expression:
nCr = (100 * 99 * 98 * ... * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (96 * 95 * 94 * ... * 3 * 2 * 1))
The result of this calculation will give us the total number of ways to select four fishes from a population of 100.
Please note that I have provided the steps to calculate the total number of ways to select four fishes from a population of 100. To calculate the probability, you would need additional information, such as whether the selection is done with or without replacement, and whether all fishes have an equal chance of being selected.
To find the probability of selecting four fishes from a pond with a population of 100, we can use the concept of combinations.
In this case, we need to find the number of combinations of 4 fishes from a population of 100. The formula to calculate combinations is given by:
nCk = n! / (k!(n-k)!)
Where n is the total number of objects to choose from, and k is the number of objects to be chosen.
In this case, n is 100 (total population) and k is 4 (number of fishes the biologist wants to select). So, we can substitute these values into the formula:
100C4 = 100! / (4!(100-4)!)
Now, let's calculate the value of this expression:
100! = 100 × 99 × 98 × 97 × .... × 3 × 2 × 1
4! = 4 × 3 × 2 × 1
(100-4)! = 96 × 95 × 94 × .... × 3 × 2 × 1
Calculating the values:
100! = 3.402823 × 10^67 (approximately)
4! = 24
(100-4)! = 9.718781 × 10^148 (approximately)
Substituting these values:
100C4 = (3.402823 × 10^67) / ((24) × (9.718781 × 10^148))
Calculating this expression:
100C4 ≈ 715,181
Therefore, the probability of selecting four fishes is approximately 1 in 715,181 when choosing from a population of 100 fishes.