The probability that an MBA aspirant will join IIM is `2/5` and that he will join XLRI is `1/3`. find the probability that he will join IIM or XLRI.

Options

A. `4/15`
B. `7/15`
C. `11/15`
D. `8/15`

Answer

To solve the problem of finding the probability that an MBA aspirant will join either IIM or XLRI, we can follow these steps:

### Step 1: Understand the given probabilities
We are given:
- Probability of joining IIM (P(IIM)) = 2/5
- Probability of joining XLRI (P(XLRI)) = 1/3

### Step 2: Identify the relationship between the events
Since the aspirant can join either IIM or XLRI but not both at the same time, these two events are mutually exclusive. This means that the probability of both events occurring simultaneously is zero:
- P(IIM ∩ XLRI) = 0

### Step 3: Use the formula for the probability of the union of two mutually exclusive events
For mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities:
- P(IIM ∪ XLRI) = P(IIM) + P(XLRI)

### Step 4: Substitute the given probabilities into the formula
Now we substitute the values we have:
- P(IIM ∪ XLRI) = P(IIM) + P(XLRI) = (2/5) + (1/3)

### Step 5: Find a common denominator to add the fractions
To add the fractions, we need a common denominator. The least common multiple (LCM) of 5 and 3 is 15. We convert each fraction:
- (2/5) = (2 * 3) / (5 * 3) = 6/15
- (1/3) = (1 * 5) / (3 * 5) = 5/15

### Step 6: Add the fractions
Now we can add the two fractions:
- P(IIM ∪ XLRI) = 6/15 + 5/15 = (6 + 5) / 15 = 11/15

### Step 7: State the final answer
Thus, the probability that the MBA aspirant will join either IIM or XLRI is:
- P(IIM ∪ XLRI) = 11/15

### Final Answer:
The probability that the MBA aspirant will join IIM or XLRI is **11/15**.

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