Final answer:
To determine the probability of events related to Courtney's laps, we apply the basic rules of probability. The probability of Courtney running no laps is 8%, the probability of running at least four laps can be found by calculating the complement of the sum of probabilities for running fewer laps, and the probability of running exactly four laps is calculated by using the probabilities of completing each lap and stopping before the next.
Step-by-step explanation:
The question posed is based on probability concepts, specifically dealing with the likelihood of events occurring in a series of independent trials. Courtney has an 8 percent chance to stop running at the start of each lap, including the very first one. The following are the calculations for parts (a), (b), and (c) of the question:
- (a) The probability of running no laps: Since there is always an 8 percent chance that Courtney will stop running before any lap, including the first, the probability that she will run no laps is simply 0.08 or 8 percent.
- (b) The probability of running at least four laps: To calculate this, we need to consider the complementary probability, which is the probability that Courtney will run fewer than four laps. This probability can be calculated by adding the probabilities of running zero, one, two, or three laps. The complement of this sum will be the probability of Courtney running at least four laps.
- Now, add these probabilities together and subtract from 1 to get the probability of running at least four laps.
- (c) The probability of running exactly four laps: To find this, we calculate the probability that Courtney completes four laps and then stops before the fifth. This is found by raising the probability of completing a lap (which is the complement of quitting, 0.92) to the power of four, and then multiplying by the probability of quitting, which is 0.08.