. Mrs. Crenshaw has confiscated 4 cell phones from 4 different students because they used them during class. To get the cell phones back, they have to answer the fol- lowing question: What is the probability that no student receives his or her own phone if Mrs. Crenshaw hands them back at random at the end of the school day? What answer should they give?
the probability that no student will get there own phone is 25%
Hope this helps!
From Miststar of Riverclan on youtube
To find the probability that no student receives their own phone, we can use the concept of derangements. A derangement is a permutation of a set where no element appears in its original position.
There are a total of 4 students and 4 cell phones. Initially, there are 4! (4 factorial) ways to distribute the phones back to the students. This equals 4 x 3 x 2 x 1 = 24 possible arrangements.
Now, let's calculate the number of favorable arrangements where no student receives their own phone. This is denoted by the symbol "!", which represents the number of derangements.
For n items, the number of derangements can be calculated using the formula: D(n) = n!(1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!).
For n = 4, the calculation becomes: D(4) = 4!(1 - 1/1! + 1/2! - 1/3! + 1/4!) = 4 x (1 - 1 + 1/2 - 1/6 + 1/24) = 4 x 9/24 = 9.
Therefore, there are 9 favorable arrangements where no student receives their own phone out of the 24 possible arrangements.
To find the probability, divide the number of favorable arrangements by the total number of possible arrangements: P = favorable arrangements / total arrangements = 9/24 = 3/8.
So, the students should give the answer 3/8 as the probability that no student receives his or her own phone.