Question
3 There are 54 fish in a rank. Some of the fish are white and the rest of the fish are red. Jeevan takes at random a fish from the tank. The probability that he takes a white fish is \( \frac{4}{9} \) (a) Work out the number of white fish originally in the tank.
Ask by O'Quinn Wright. in Egypt
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There were 24 white fish originally in the tank.
Solution
To determine the number of white fish originally in the tank, let's break down the information given:
1. **Total Fish in the Tank:** 54
2. **Probability of Picking a White Fish:** \( \frac{4}{9} \)
Let \( W \) represent the number of white fish in the tank. The probability of picking a white fish is given by the ratio of white fish to the total number of fish:
\[
\frac{W}{54} = \frac{4}{9}
\]
To solve for \( W \), multiply both sides of the equation by 54:
\[
W = \frac{4}{9} \times 54
\]
Simplify the calculation:
\[
W = 4 \times 6 = 24
\]
**Therefore, there were 24 white fish originally in the tank.**
**Answer:** 24
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the number of white fish originally in the tank, we can use the probability given. Let \( W \) be the number of white fish. According to the problem, the probability of picking a white fish is \( \frac{4}{9} \). This probability can be expressed as: \[ \frac{W}{54} = \frac{4}{9} \] Now, we can cross-multiply to solve for \( W \): \[ 9W = 54 \times 4 \] \[ 9W = 216 \] \[ W = \frac{216}{9} = 24 \] So, there are 24 white fish originally in the tank. To find the number of red fish, we simply subtract the number of white fish from the total: \[ 54 - 24 = 30 \] Thus, there are 30 red fish in the tank.
