In a statistics class of 45 students, 12 have a strong intrest in statistics. If two students are selected at random from this class, what is the propability that both of them have a strong interest in statisitcs?

first one 12/45

second on 11/44

12/45 * 11/44

To find the probability that both students have a strong interest in statistics, we need to use the concept of probability. Here's how you can calculate it:

Step 1: Determine the number of students with a strong interest in statistics.
In this case, there are 12 students with a strong interest.

Step 2: Determine the total number of students in the class.
The class has a total of 45 students.

Step 3: Calculate the probability of selecting the first student with a strong interest.
Since there are 12 students with a strong interest out of 45, the probability of selecting the first student with a strong interest is 12/45.

Step 4: Calculate the probability of selecting the second student with a strong interest.
After selecting the first student, there are 11 students with a strong interest left out of the remaining 44 students (assuming the first student is not replaced). Therefore, the probability of selecting the second student with a strong interest is 11/44.

Step 5: Multiply the probabilities from Step 3 and Step 4.
To find the probability that both students selected have a strong interest, you need to multiply the probabilities calculated in the previous steps: (12/45) * (11/44).

Step 6: Calculate the final probability.
Multiply the fractions and simplify if possible. In this case, the probability is (12/45) * (11/44) = 0.0556 or approximately 5.6%. Therefore, the probability that both students selected have a strong interest in statistics is 5.6%.