Question

Probability of getting odd numbers in first 100 numbers.

Answer 1

In this problem, we are asked to find the probability of getting an odd number when choosing a number randomly from the first 100 numbers (i.e., numbers from 1 to 100).

Step 1: Total Number of Possible Outcomes

The total number of outcomes in this case is the total number of numbers in the range from 1 to 100. This means there are 100 possible outcomes (since we are considering the first 100 numbers).

Step 2: Number of Odd Numbers

Odd numbers are those numbers that are not divisible by 2. The odd numbers between 1 and 100 are:

1, 3, 5, 7, ..., 97, 99

These odd numbers form a sequence where the first term is 1, the common difference is 2, and the last term is 99. The number of terms (odd numbers) in this sequence is 50.

Step 3: Probability Formula

The probability of an event is given by the formula:

Probability = \(\frac { \text{Number of desired outcomes} }{ \text{Total number of possible outcomes} }\)

Step 4: Substituting Values

The number of odd numbers is 50, and the total number of possible outcomes is 100. So, the probability of getting an odd number is:

Probability = \(\frac {50}{100}\)

Step 5: Simplification

The fraction \(\frac {50}{100}\) can be simplified to \(\frac {1}{2}\). Therefore, the probability of getting an odd number is:

Probability = \(\frac {1}{2}\)

Conclusion

So, the probability of randomly selecting an odd number from the first 100 numbers is \(\frac {1}{2}\), or 0.5.