We can find total number of observations between 3 and 100 which are divisible by 7 using A.P. Technique.we will have A.P. as:7,14,21,.......,98a=7d=7Tn=98Now, Tn=a+(n-1)d98=7+(n-1)798=7+7n-798=7nso,n=14so, Total number of favourable outcomes =14similarly,Using A.P. technique Total no. of possible outcomes=98so,P (E)=14/98 =1/7

**Probability of getting a number between 3 and 100 which is divisible by 7**

To find the probability of getting a number between 3 and 100 that is divisible by 7, we need to determine the total number of favorable outcomes and the total number of possible outcomes.

**Total Number of Possible Outcomes:**

The total number of possible outcomes is the total number of integers between 3 and 100, inclusive. So, the range is 100 - 3 + 1 = 98.

**Total Number of Favorable Outcomes:**

To determine the total number of favorable outcomes, we need to find the count of integers between 3 and 100 that are divisible by 7.

Divisible by 7: The first number divisible by 7 in this range is 7 itself. The last number divisible by 7 is 98 (since 7 * 14 = 98). So, there are 14 integers divisible by 7 in this range.

**Calculating Probability:**

Now that we have the total number of favorable outcomes (14) and the total number of possible outcomes (98), we can calculate the probability.

Probability = (Total number of favorable outcomes) / (Total number of possible outcomes)

Probability = 14 / 98

Simplifying the fraction, we get:

Probability = 1 / 7

Thus, the probability of getting a number between 3 and 100 that is divisible by 7 is 1/7.

In conclusion, when randomly selecting a number between 3 and 100, there is a 1/7 probability that the chosen number will be divisible by 7.