Final answer:
In summary, the pair of events that are dependent is drawing a black sock from a drawer and then drawing another without replacement. This is because the first event changes the conditions for the second, affecting its probability.
Step-by-step explanation:
Whether two events are dependent or independent affects the calculation of their probability. Independent events have no impact on the likelihood of each other occurring, while dependent events do.
- Event a (flipping a coin twice) involves independent events because the outcome of the first flip does not affect the second flip's outcome.
- Event b (drawing a friend's name from a hat, replacing it, and drawing again) also involves independent events as the outcome of the first draw is not affected by the second, thanks to the replacement.
- Event c (spinning a numbered spinner twice) is another example of independent events since the result of the first spin does not affect the second spin.
- Event d (removing black socks from a drawer one after another without replacement) involves dependent events because the outcome of the first draw affects the probability of the second; removing one sock changes the total number of socks, which affects the chances of drawing a black sock again.
Thus, Event d is the pair of dependent events.