teresa and julia are among 10 students who have applied for a trip to washington DC. Two students from the group will be selected at random for the trip. What is the probability that teresa and julia will be the 2 students selected
/
With 10 students you have 10 choices for the first student to go, then 9 choices for the second student to go. That would seem to be 90 ways to choose the people to go on the trip. But the order doesn't matter. You don't care if Alice is chosen, then Bob, or vice versa. So divide this number by 2 to account for the double-counting.
There are 45 ways to pick the 2 people out of 10.
C(10,2) = (10 x 9) / (2 x 1) = 45 ways
Selecting Teresa and Julia is just one of those possible outcomes, so the probability is:
1/45
To calculate the probability, we need to divide the number of favorable outcomes by the total number of possible outcomes.
In this scenario, there are 10 students in total, and 2 students will be selected randomly for the trip. We want to find the probability that Teresa and Julia are the 2 students selected.
The number of favorable outcomes is 1, as there is only one way for Teresa and Julia to be selected together.
The total number of possible outcomes can be calculated using the combination formula, as order does not matter in this case. We need to choose 2 students from a group of 10, so the total number of possible outcomes is given by:
C(10,2) = 10! / (2! * (10-2)!) = 45
Now, we can calculate the probability:
Probability (Teresa and Julia selected) = Number of favorable outcomes / Total number of possible outcomes
= 1 / 45
Therefore, the probability that Teresa and Julia will be the 2 students selected for the trip is 1/45, or approximately 0.0222, if rounded to four decimal places.
To calculate the probability that Teresa and Julia will be the 2 students selected for the trip, we need to find the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes: Since two students are being selected at random from a group of 10 students, the total number of possible outcomes is the number of ways to choose 2 students out of 10, which can be calculated using the combination formula:
C(10, 2) = 10! / (2! * (10-2)!) = 45
Number of favorable outcomes: Since we want Teresa and Julia to be the 2 selected students, there is only 1 way to choose them out of the group of 10 students.
So the number of favorable outcomes is 1.
Now we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 45
Therefore, the probability that Teresa and Julia will be the 2 students selected for the trip is 1/45.