Question

An aquarium contains 4 goldfishes, 6 swordtails and 10 tetras. What is the probability that a fish randomly selected is a goldfish or a tetra ?

• A. 2/7
• B. 5/7
• C. 7/10
• D. 1/4

Hint:

Always start probability questions by calculating the total size of the sample space (here, 20). Then, add the counts of the desired mutually exclusive outcomes (4 + 10 = 14) and simplify the fraction (\(14/20 = 7/10\)).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Probability is a measure of the likelihood that an event will occur, calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.
When two events are mutually exclusive (they cannot occur at the same time, such as selecting a single fish that is both a goldfish and a tetra), the probability of either event occurring is the sum of their individual probabilities.
Key Formula or Approach:
The probability of selecting a goldfish or a tetra is given by:
\[ P(\text{Goldfish or Tetra}) = \frac{\text{Number of Goldfishes} + \text{Number of Tetras}}{\text{Total Number of Fish}} \]

Step 2: Detailed Explanation:
Let us calculate the values from the given problem:
- Number of Goldfishes = \(4\)
- Number of Swordtails = \(6\)
- Number of Tetras = \(10\)
First, calculate the total number of fish in the aquarium:
\[ \text{Total Number of Fish} = 4 + 6 + 10 = 20 \]
Next, determine the number of favorable outcomes (selecting either a goldfish or a tetra):
\[ \text{Favorable Outcomes} = 4\text{ (Goldfishes)} + 10\text{ (Tetras)} = 14 \]
Now, calculate the probability:
\[ P(\text{Goldfish or Tetra}) = \frac{14}{20} \]
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2:
\[ P(\text{Goldfish or Tetra}) = \frac{7}{10} \]
Therefore, the probability of selecting a goldfish or a tetra is 7/10.

Step 4: Final Answer:
The probability of randomly selecting a goldfish or a tetra is 7/10, which corresponds to Option (C).