A JEE aspirant estimates that she will be successful with an 80 percent chance if she studies 10 hours per day, with a 60 percent chance if she studies 7 hours per day and with 40 percent chance if she studies 4 hours per day. She further believes that she will study 10 hours, 7 hours and 4 hours per day with probabilities 0.1, 0.2 and 0.7 respectively. The chance she will be successful is: a. 0.28 b. 0.38 c. 0.48 d. 0.58

Options

A. 0.28
B. 0.38
C. 0.48
D. 0.58

Answer

To find the overall probability of success for the JEE aspirant based on her study hours and their respective probabilities, we can use the law of total probability. Here’s the step-by-step solution:

### Step 1: Identify the probabilities and chances of success
- Probability of studying 10 hours = 0.1, Chance of success = 80% = 0.8
- Probability of studying 7 hours = 0.2, Chance of success = 60% = 0.6
- Probability of studying 4 hours = 0.7, Chance of success = 40% = 0.4

### Step 2: Calculate the probability of success for each scenario
- For studying 10 hours:
\[ P(\text{Success | 10 hours}) = 0.1 \times 0.8 = 0.08 \]

- For studying 7 hours:
\[ P(\text{Success | 7 hours}) = 0.2 \times 0.6 = 0.12 \]

- For studying 4 hours:
\[ P(\text{Success | 4 hours}) = 0.7 \times 0.4 = 0.28 \]

### Step 3: Sum the probabilities of success from all scenarios
Now, we add the probabilities calculated in Step 2:
\[ P(\text{Success}) = P(\text{Success | 10 hours}) + P(\text{Success | 7 hours}) + P(\text{Success | 4 hours}) \]
\[ P(\text{Success}) = 0.08 + 0.12 + 0.28 = 0.48 \]

### Conclusion
The overall probability that the JEE aspirant will be successful is **0.48**.

### Final Answer
The correct option is **c. 0.48**.