Question

Each of 4 students randomly chooses one of 4 calculus sections to take.

(a) What is the probability that they all choose the same section?
a) 1/16
b) 1/4
c) 1/2
d) 3/4
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Answer 1

The probability that all four students choose the same section is 1/64.

Step-by-step explanation:

The probability that all four students choose the same section can be calculated as follows:

Since each student has 4 choices to make, and they choose randomly, there are a total of 4*4*4*4 = 256 possible outcomes.

Out of these, there are 4 outcomes where all four students choose the same section (e.g., all four choose section 1, or all four choose section 2, etc.).

Therefore, the probability is 4/256 = 1/64.