To solve this problem, we first need to break down the information given in the scenario:
- Total students surveyed: 275
- Number of vegetarians: 20
- Vegetarians eating both fish and eggs: 9
- Vegetarians eating only eggs (not fish): 3
- Vegetarians eating neither fish nor eggs: 8
However, there seems to be a discrepancy here. If we look at the vegetarians:
- 9 (both fish and eggs) + 3 (only eggs) + x (eating neither) = 20
This suggests that there are only 8 that eat neither, which means our count of 20 vegetarians matches appropriately:
- 9 + 3 + 8 = 20
Now, to find the probability that a randomly chosen vegetarian eats fish, we look at the number of vegetarians who eat fish:
- Number of vegetarians who eat fish (both types): 9
- Total number of vegetarians: 20
The probability (P) can be calculated using the formula:
P(Eating Fish | Vegetarian) = (Number of vegetarians who eat fish) / (Total number of vegetarians)
P(Eating Fish | Vegetarian) = 9 / 20 = 0.45
Therefore, the probability that a randomly chosen vegetarian student eats fish is 0.45, or 45%.