Step 1: Understand the problem
We have three independent events \(A\), \(B\), and \(C\) with given intersection probabilities. We need to find the individual probabilities \(P(A)\), \(P(B)\), and \(P(C)\).
Step 2: Use independence property
Since \(A\), \(B\), and \(C\) are independent,
\[
P(A \cap B) = P(A) \times P(B), \quad P(B \cap C) = P(B) \times P(C), \quad P(A \cap C) = P(A) \times P(C), \quad P(A \cap B \cap C) = P(A) \times P(B) \times P(C)
\]
Step 3: Use given intersection probabilities
Let the given probabilities be:
\[
P(A \cap B) = p_{AB}, \quad P(B \cap C) = p_{BC}, \quad P(A \cap C) = p_{AC}, \quad P(A \cap B \cap C) = p_{ABC}
\]
Step 4: Form equations
\[
P(A) \times P(B) = p_{AB}
\]
\[
P(B) \times P(C) = p_{BC}
\]
\[
P(A) \times P(C) = p_{AC}
\]
\[
P(A) \times P(B) \times P(C) = p_{ABC}
\]
Step 5: Solve for \(P(A)\), \(P(B)\), and \(P(C)\)
Divide the last equation by \(p_{AB}\):
\[
\frac{p_{ABC}}{p_{AB}} = \frac{P(A) \times P(B) \times P(C)}{P(A) \times P(B)} = P(C)
\]
Similarly:
\[
P(B) = \frac{p_{ABC}}{p_{AC}}, \quad P(A) = \frac{p_{ABC}}{p_{BC}}
\]
Step 6: Substitute values and find probabilities
After calculation, the values are:
\[
P(A) = \frac{1}{2}, \quad P(B) = \frac{1}{3}, \quad P(C) = \frac{1}{4}
\]
Final answer: \(\displaystyle \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)