A teacher has assigned numbers 1-8 to eight students in a classroom. The numbers of all the students are put in a basket. The teacher selects a number and replaces it in the basket. Then the teacher selects a second number. Find P(student 1, then student 8).
1/16
1/64
1/4
1/56
clearly, prob = (1/8)(1/8) = ...
1/64
(1/8)(1/8) = 1/64
To find the probability of student 1 being selected first and then student 8 being selected next, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
Since there are 8 students in the classroom, the total number of outcomes is 8.
Favorable Outcomes:
To find the number of favorable outcomes, we need to consider the following:
- Student 1 is selected first (1 possible outcome).
- After replacing the number, student 8 is selected next (1 possible outcome).
According to the multiplication principle of counting, we multiply the number of outcomes for each event to find the total number of favorable outcomes.
Therefore, the number of favorable outcomes is 1 * 1 = 1.
Probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of outcomes.
So, the probability of student 1 being selected first and then student 8 being selected next is 1/8.
Therefore, the correct answer is not provided among the options given.