Final answer:
To find the probability of different scenarios related to a basketball player's free throw shots, we can use the concept of independent events. For each scenario, we multiply or add the probabilities based on the given information.
Step-by-step explanation:
To find the probability that the student's first successful free throw is shot number five, we first need to find the probability of missing the first four shots and then making the fifth shot. As each shot is an independent event, we can multiply the probabilities together. The probability of missing a free throw is 1 - 0.8 = 0.2, so the probability of missing four shots in a row is (0.2)^4. Therefore, the probability of making the fifth shot is 1 - (0.2)^4.
To find the probability that the student makes her first successful free throw within the first two shots, we need to find the probability of making the first shot or making the second shot. Again, these are independent events, so we can add the probabilities together. The probability of making a free throw is 0.8, so the probability of making the first or second shot is 0.8 + (0.2 * 0.8) = 0.8 + 0.16 = 0.96.
To find the probability that the student takes more than five shots to make her first successful free throw, we need to find the probability of missing the first five shots. Again, the probability of missing a free throw is 0.2, so the probability of missing five shots in a row is (0.2)^5. Therefore, the probability of taking more than five shots to make the first successful free throw is 0.2^5.