Question

(d) experiment 4: a box contains pens. some pens have ink and some do not. a teacher randomly selects a pen and sets it aside. then another random selection is made from the remaining pens.
event a: the first selection is a pen with ink.
event b: the second selection is a pen with no ink.
determine whether events a and b are independent or dependent.
○ independent ○ dependent
(e) experiment 5: at the beginning of each of two football games, a coin is tossed, and the winner of the coin toss is determined.
event a: in the first game, the home team wins the coin toss.
event b: in the second game, the visiting team wins the coin toss.
determine whether events a and b are independent or dependent.
○ independent ○ dependent

Explanation:

(d)

Step1: Analyze the first experiment

In Experiment 4, when the first pen is selected (Event A), the number of pens for the second selection changes. If Event A occurs (a pen with ink is taken first), the composition of pens left (for Event B) is different than if Event A did not occur.

Step2: Determine dependence

Since the outcome of Event A affects the probability of Event B (because the sample - space for the second selection is altered based on the first selection), the events are dependent.

(e)

Step1: Analyze the second experiment

In Experiment 5, the coin - toss in the first game (Event A) has no impact on the coin - toss in the second game (Event B). The probability of the visiting team winning the coin - toss in the second game is not affected by who won the coin - toss in the first game. The two coin - tosses are separate and independent trials.

Step2: Determine independence

Since the outcome of Event A does not affect the probability of Event B, the events are independent.

Answer:

(d) Dependent
(e) Independent