Question

(a) experiment 1: a litter of puppies consists of black puppies and white puppies. a puppy is randomly selected and removed from the litter. then another random selection is made from the remaining puppies. event a: the first selection is a black puppy. event b: the second selection is a white puppy. determine whether events a and b are independent or dependent. independent dependent (b) experiment 2: a family has two children. event a: the older child has brown eyes. event b: both children have brown eyes. determine whether events a and b are independent or dependent. independent dependent (c) experiment 3: a hat contains slips of paper with the names of boys and girls in a class. a name is randomly selected and returned to the hat. then another random selection is made. event a: the first selection is a boy. event b: the second selection is a girl. determine whether events a and b are independent or dependent. independent dependent

Explanation:

(a)

Step1: Analyze the first experiment

In Experiment 1, when the first puppy (black) is removed, the composition of the litter changes. The probability of selecting a white puppy (Event B) is affected by the outcome of Event A (selecting a black puppy first).

Step2: Determine dependence

Since the probability of Event B changes based on the occurrence of Event A, the events are dependent.

(b)

Step1: Analyze the second experiment

In Experiment 2, if the older child does not have brown eyes (non - occurrence of Event A), then Event B (both children have brown eyes) cannot occur. The probability of Event B is influenced by Event A.

Step2: Determine dependence

Because the outcome of Event A impacts the possibility of Event B, the events are dependent.

(c)

Step1: Analyze the third experiment

In Experiment 3, since the first - selected name is returned to the hat, the composition of the hat remains the same for the second selection. The probability of selecting a girl (Event B) is not affected by the first selection (Event A).

Step2: Determine independence

As the probability of Event B is unchanged regardless of Event A, the events are independent.

Answer:

(a) Dependent
(b) Dependent
(c) Independent