Probability of Running Around Laps The question is as follows: 


  Jack is supposed to run laps around the outdoor track. At the start of each lap, including the first, there is always an $8$ percent chance that Jack will not run for the day. What is the probability that Jack will run (a) no laps? (b) at least four laps? (c) exactly four laps? 


(a) 
 The chances of running no laps is $8$%, or $\frac{2}{25}$. 

(b) The chances of running at least four laps is $(\frac{23}{25})^4$. 

I am not completely sure about (c), especially in making sure whether he will run the exact four laps. 

If there are any errors, please let me know. Any help will be greatly appreciated.
You are correct so far.  For c, he needs to run at least four laps, which is your answer to b, and then run no more laps, which is your answer to a.
In order to run exactly 4 laps he must run

a) the first lap which has probability, as you say, 2/25

b) the second lap which also has probability 2/25

c) the third lap which also has probability 2/25

d) the fourth lap which also has probability 2/25

e) NOT run the fifth lap which has probability 23/25.

The probability of running exactly 4 laps is $\left(\frac{2}{25}\right)^4\left(\frac{23}{25}\right)$