Model and solve problems that involve probability, with and without technology.

A quality control inspector examines a batch of electronic components. Historical data shows that \(3\%\) of components have a manufacturing defect. The inspector tests components one at a time until a defective component is found. (a) Model this situation using an appropriate probability distribution. State the probability that the inspector finds the first defective component on the fifth test. [2 marks] (b) Determine the probability that the inspector needs to test more than eight components before finding the first defect. [2 marks]

A local sports club runs a training program where participants attempt basketball free throws. Historical data shows that a participant has a probability of 0.6 of successfully making a free throw. In a practice session, a participant attempts 10 free throws. Calculate the probability that the participant makes exactly 7 successful free throws.

A biathlon athlete completes a training program where she attempts accuracy shots. Historical data shows that she hits the target with probability $p = 0.75$ on each independent shot. In a competition consisting of 8 shots, which calculation correctly models the probability that she hits exactly 6 of the 8 shots?