Give an example of two events that are independent and an example of two events that are dependent.
Gwen sold her car on consignment for x dollars. The saleswoman's commission was 10% of the selling price and Gwen received $6570.
My birthday and your birthday.
I have two pennies and two dimes in my pocket. What is the probability of my reaching into my pocket twice for a coin and pulling out a penny first and then a dime?
Don, It would help if you click on "post a new question" above instead of posting a question as an answer to veronica.
6570 = .9 x
x = 6570/.9
thank you so much Damon
To understand the difference between independent and dependent events, let's start with an example of independent events:
Example 1: Independent Events
Let's say we have two events: flipping a fair coin and rolling a fair six-sided die. These two events are considered independent because the outcome of one event does not affect the outcome of the other.
When flipping the coin, the possible outcomes are heads (H) or tails (T). Similarly, when rolling the die, the possible outcomes are numbers 1 through 6. The probability of getting heads on the coin flip does not change depending on the outcome of the die roll, and vice versa. Thus, these events are considered independent.
Now, let's move on to an example of dependent events:
Example 2: Dependent Events
Let's consider drawing two cards from a standard deck without replacement (not putting the first card back before drawing the second). In this case, the events are dependent because the outcome of the first card draw affects the probability of the second card's outcome.
Suppose we want to find the probability of drawing two red cards in a row. Initially, the deck contains 26 red cards and 26 black cards. After drawing the first card, the deck changes, reducing the number of available red and black cards for the second draw.
For instance, if the first card drawn is red, there will be 25 red cards and 26 black cards left for the second draw. However, if the first card drawn is black, there will be 26 red cards and 25 black cards left for the second draw. Thus, the probability of drawing two red cards in a row depends on the outcome of the first draw, making these events dependent.
In summary, independent events are those in which the outcome of one event does not affect the outcome of the other. On the other hand, dependent events are those in which the outcome of one event influences the probability of the other event.