Keshawn and Samantha are in a science class with 18 other students. The teacher randomly divides the class into 10 pairs of laboratory partners. Whar is the probability that Keshawn and Samantha are lab partners?
Keshawn has 19 other potential partners with equal probablility of each. (That is because there is a total of 20 students). What does that tell you?
he has a probability of 1:19?
is 1:19 the correct answer? Because, the more I think about it, the more confused I get since there are 20 students in the class, but it has to be 19, since Keshawn can't be partnered with himself, right?
To find the probability of Keshawn and Samantha being lab partners, we need to determine the total number of possible pairs that can be formed and the number of pairs that include Keshawn and Samantha together.
First, let's consider the total number of pairs that can be formed. Since there are 20 students in total (Keshawn, Samantha, and the other 18 students), we need to choose 2 students from this group for each pair. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n - r)!)
In this case, n = 20 (the total number of students) and r = 2 (the number of students in each pair).
C(20, 2) = 20! / (2!(20-2)!)
= 20! / (2!18!)
= (20 * 19 * 18!) / (2! * 18!)
= (20 * 19) / 2
= 190
So, there are 190 possible pairs that can be formed.
Next, let's calculate the number of pairs that include Keshawn and Samantha together. Since they are fixed partners, we need to choose the remaining partner from the remaining 18 students. This can also be calculated using the combination formula:
C(n, r) = n! / (r!(n - r)!)
In this case, n = 18 (the remaining students) and r = 1 (the number of students we need to choose to form the pair with Keshawn and Samantha).
C(18, 1) = 18! / (1!(18-1)!)
= 18! / (1! 17!)
= 18
So, there are 18 pairs that include Keshawn and Samantha together.
Finally, the probability of Keshawn and Samantha being lab partners can be calculated by dividing the number of pairs that include Keshawn and Samantha together by the total number of possible pairs:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 18 / 190
= 9 / 95
≈ 0.0947 or 9.47% (rounded to two decimal places)
Therefore, the probability that Keshawn and Samantha are lab partners is approximately 0.0947 or 9.47%.