In a group of equal number of men and women 10% men and 45% women are unemployed. What is the probability that a person selected at random is employed ?

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the total number of men and women.
Assume there are 100 men and 100 women in the group.

### Step 2: Calculate the number of unemployed men.
Given that 10% of men are unemployed:
- Unemployed men = 10% of 100 = 10 men.

### Step 3: Calculate the number of employed men.
Since there are 100 men in total, the number of employed men is:
- Employed men = Total men - Unemployed men = 100 - 10 = 90 men.

### Step 4: Calculate the number of unemployed women.
Given that 45% of women are unemployed:
- Unemployed women = 45% of 100 = 45 women.

### Step 5: Calculate the number of employed women.
Since there are 100 women in total, the number of employed women is:
- Employed women = Total women - Unemployed women = 100 - 45 = 55 women.

### Step 6: Calculate the total number of employed people.
The total number of employed people is the sum of employed men and employed women:
- Total employed = Employed men + Employed women = 90 + 55 = 145.

### Step 7: Calculate the total number of people in the group.
The total number of people (men + women) is:
- Total people = Total men + Total women = 100 + 100 = 200.

### Step 8: Calculate the probability that a person selected at random is employed.
The probability (P) that a randomly selected person is employed is given by the formula:
\[ P(\text{Employed}) = \frac{\text{Total employed}}{\text{Total people}} \]
Substituting the values we found:
\[ P(\text{Employed}) = \frac{145}{200} \]

### Step 9: Simplify the probability.
To simplify:
\[ P(\text{Employed}) = \frac{145 \div 5}{200 \div 5} = \frac{29}{40} \]

Thus, the probability that a person selected at random is employed is:
\[ \frac{29}{40} \]