for each experiment, determine whether events a and b are independent or dependent. experiment events…

for each experiment, determine whether events a and b are independent or dependent. experiment events independent dependent 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. a family has two children. event a: the older child has brown eyes. event b: both children have brown eyes. 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. 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. 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.

for each experiment, determine whether events a and b are independent or dependent. experiment events independent dependent 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. a family has two children. event a: the older child has brown eyes. event b: both children have brown eyes. 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. 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. 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.

Answer

Answer:

  1. Dependent
  2. Dependent
  3. Independent
  4. Dependent
  5. Independent

Explanation:

Step1: First - Puppy selection

The first puppy selection changes the composition of the litter for the second selection. So, the probability of the second - event depends on the first - event.

Step2: Children's eye - color

If the older child has brown eyes, it affects the probability of both children having brown eyes. So, event B depends on event A.

Step3: Name selection from hat

Since the name is returned to the hat after the first selection, the probability of the second selection is not affected by the first selection.

Step4: Pen selection

The first pen selection changes the number and types of pens left for the second selection. So, the second - event depends on the first - event.

Step5: Coin - toss in football games

The result of the first coin - toss does not affect the result of the second coin - toss. Each coin - toss is an independent event with a probability of 0.5 for each outcome.