In a class, 40% of students study maths and science and 60 % of student study maths. What is the probability of a student studying science given the student is already studying maths?

Options

A. `(1)/(3)`
B. `(1)/(6)`
C. `(2)/(3)`
D. `(1)/(5)`

Answer

To solve the problem step by step, we can use the concept of conditional probability. We need to find the probability of a student studying Science given that the student is already studying Maths.

### Step 1: Define the Events
Let:
- \( M \) = Event that a student studies Maths
- \( S \) = Event that a student studies Science

### Step 2: Identify Given Probabilities
From the problem statement, we know:
- \( P(M \cap S) = 0.4 \) (Probability that a student studies both Maths and Science)
- \( P(M) = 0.6 \) (Probability that a student studies Maths)

### Step 3: Use the Formula for Conditional Probability
We need to find \( P(S | M) \), which is the probability of a student studying Science given that the student studies Maths. The formula for conditional probability is given by:

\[ P(S | M) = \frac{P(M \cap S)}{P(M)} \]

### Step 4: Substitute the Known Values
Now, we can substitute the values we have into the formula:

\[ P(S | M) = \frac{P(M \cap S)}{P(M)} = \frac{0.4}{0.6} \]

### Step 5: Simplify the Expression
Now we simplify the fraction:

\[ P(S | M) = \frac{0.4}{0.6} = \frac{4}{6} = \frac{2}{3} \]

### Step 6: Conclusion
Thus, the probability of a student studying Science given that the student is already studying Maths is:

\[ P(S | M) = \frac{2}{3} \]