Question

Which of these pairs of events are dependent?

a. You flip a coin and get tails. You flip it a second time and get heads.
b. You pull your friend's name out of a hat that holds 20 different names, replace
name, then draw out your friend's name again.
c. You spin a spinner divided into five equal parts and is numbered 1-5. You get a 3 on the first spin, and then spin again and get a 2 on the second spin.
d. You remove a black sock from a drawer without looking, then remove another black
sock.​

Answer 1

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.

Answer 2

d

Step-by-step explanation:

a, b, and c are independent, because they don't necessarily affect the probability of each other.