Determine whether the events are Independent or Dependent. Sort the questions into the appropriate category. 4 questions are independent and 4 questions are dependent.
Question A: Flipping a coin and tossing a die
Question B: Picking two digits from 0 to 9 when the digits cannot repeat
Question C: Picking two books out of 10 books to read for an English class Question D: Drawing a card from a 52 card deck then drawing a second card after replacing the first card
Question E: From a group of 5 friends, choosing a person to drive and another a person to sit in the passenger seat
Question F: Drawing a card from a 52 card deck then drawing a second card without replacing the first card
Question G: Picking two digits from 0 to 9 when the digits can repeat Question H: Flipping a coin and then flipping the coin again
To determine whether events are independent or dependent, we need to understand the concept of independence and dependence.
Independent events are events that do not affect each other's outcomes. In other words, the outcome of one event does not impact the outcome of the other.
Dependent events, on the other hand, are events that do affect each other's outcomes. The outcome of one event can impact the outcome of the other.
Now, let's analyze each question to determine whether it falls under the category of independent or dependent events:
Question A: Flipping a coin and tossing a die.
These two events, flipping a coin and tossing a die, are independent of each other. The outcome of the coin flip does not affect the outcome of the die toss, and vice versa. Therefore, this question represents independent events.
Question B: Picking two digits from 0 to 9 when the digits cannot repeat.
In this case, the events are dependent because the outcome of the first digit selected affects the possibilities for the second digit selection. After selecting the first digit, there are fewer options available for the second digit. Hence, this question represents dependent events.
Question C: Picking two books out of 10 books to read for an English class.
Since the books are not replaced after being selected, the second book selection is dependent on the outcome of the first book selection. The outcome of selecting the first book affects the pool of available options for the second selection. Therefore, this question represents dependent events.
Question D: Drawing a card from a 52 card deck then drawing a second card after replacing the first card.
In this case, the events are independent because the first card is replaced before drawing the second card. The outcome of the first card draw does not affect the possibilities for the second card draw. Therefore, this question represents independent events.
Question E: From a group of 5 friends, choosing a person to drive and another person to sit in the passenger seat.
The events in this question are dependent. The person selected to drive affects the remaining possibilities for selecting the person to sit in the passenger seat. Hence, this question represents dependent events.
Question F: Drawing a card from a 52 card deck then drawing a second card without replacing the first card.
The events in this question are dependent because the first card drawn affects the possible outcomes for the second card draw. After the first card is drawn, there are fewer remaining cards in the deck. Therefore, this question represents dependent events.
Question G: Picking two digits from 0 to 9 when the digits can repeat.
In this case, the events are independent because the selection of one digit does not affect the possibilities for selecting the other digit. Therefore, this question represents independent events.
Question H: Flipping a coin and then flipping the coin again.
The events in this question are independent. The outcome of the first coin flip does not influence the outcome of the second coin flip. Hence, this question represents independent events.
In summary, the independent events are Question A, Question D, Question G, and Question H. The dependent events are Question B, Question C, Question E, and Question F.