Help with a simple math problem?

No, because there's four possibilities that they all select the same tire.

Then you have: 4/4^4=1/64

So, what's the numerator? The number of students? What's the denominator? the number of tires? What does the ^4 signify or represent? Sorry, I need to understand this so that I can get it right on my exam.

4/256 = 1/64

("4^4" means 4 to the 4th power)

Where'd the 4 come from? What does that represent? The number of students?

You can go about it an alternative way.

So there are P1, P2, P3, P4. The probability that P2 picks the same tire as P1 is 1/4. Similarly for P3 and P4. Therefore the probability that P2, P3, and P4 all pick the same tire as P1 is (1/4)x(1/4)x(1/4) = 1/64.

Oh, wow! I get it! Thank you so very much! It all makes sense now!

Keep in mind that the probability of a desired outcome is the number of ways the desired outcome can occur divided by the total number of possible outcomes.
4^4 is the number of ways the four students can select a tire. This is the total number of possible outcomes. There are 4 ways that all of the students can select the same tire. This is the number of ways the desired outcome can occur. Therefore, the probability is 4/4^4 = 1/4^3.

You have four tires A,B,C & D. The first student picks a tire, any tire--the reminin three students pick the same tire.

The possibilities are
AAAA, BBBB, CCCC & DDDD

the first students pick is 4/4, the remaining three are 1/4

AAAA is 1/4^4, BBBB is 1/4^4, CCCC is 1/4^4 & DDDD is 1/4^4

adding them up is the P(E), 4(1/4^4)=1/4^3

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