In a tank, there are 6 goldfishes and 3 angel fishes. What is the probability of selecting 2 gold fishes and 1 angel fish?
1/9
2/9
4/9
5/9
4/9
To find the probability of selecting 2 goldfishes and 1 angelfish, we need to determine the total number of outcomes and the number of favorable outcomes.
The total number of outcomes can be calculated by adding the number of goldfishes and the number of angelfishes together:
Total number of outcomes = number of goldfishes + number of angelfishes
= 6 + 3
= 9
Next, we need to find the number of favorable outcomes, which is the number of ways we can select 2 goldfishes and 1 angelfish.
The number of ways to select 2 goldfishes from 6 is given by the combination formula:
Number of ways to select 2 goldfishes from 6 = C(6, 2) = 6! / (2! * (6-2)!) = 15
Similarly, the number of ways to select 1 angelfish from 3 is given by:
Number of ways to select 1 angelfish from 3 = C(3, 1) = 3! / (1! * (3-1)!) = 3
To find the number of favorable outcomes, we multiply the number of ways to select 2 goldfishes by the number of ways to select 1 angelfish:
Number of favorable outcomes = Number of ways to select 2 goldfishes * Number of ways to select 1 angelfish
= 15 * 3
= 45
Therefore, the probability of selecting 2 goldfishes and 1 angelfish is:
Probability = Number of favorable outcomes / Total number of outcomes
= 45 / 9
= 5/9
So, the answer is 5/9.
To find the probability of selecting 2 goldfishes and 1 angel fish, we need to calculate the probability of each event and then multiply them together.
Step 1: Calculate the probability of selecting the first goldfish.
There are 6 goldfishes out of a total of 9 fishes in the tank. Therefore, the probability of selecting the first goldfish is 6/9.
Step 2: Calculate the probability of selecting the second goldfish.
Since we have already selected one goldfish, there are now 5 goldfishes left. The total number of fishes in the tank remains the same, which is 9. Therefore, the probability of selecting the second goldfish is 5/9.
Step 3: Calculate the probability of selecting the angel fish.
There are 3 angel fishes out of a total of 9 fishes in the tank. Therefore, the probability of selecting the angel fish is 3/9.
Step 4: Multiply the probabilities of each event.
To find the overall probability, we simply multiply the probabilities of each event together:
(6/9) * (5/9) * (3/9) = 90/729 = 10/81
Therefore, the probability of selecting 2 gold fishes and 1 angel fish is 10/81.
None of the given options (1/9, 2/9, 4/9, 5/9) match the correct answer, which is 10/81.