State whether the events described are independent or dependent and determine the probability:
A bag contains 7 red checkers and 11 black checkers. One checker is drawn and replaced. Then a second checker is drawn. What is the probability that a red checker was drawn both times?
You should not cheat on your math scantron. That is the answer.
IF YOU NOT GOING TO HELP THEN DON'T ANSWER AT ALL CARO !!!
So, I am correct. I shall tell our math teachers on you ~gero~
To determine whether the events described are independent or dependent and calculate the probability, we need to consider if the outcome of the first event affects the outcome of the second event.
In this case, the event is drawing a checker from the bag. Since the first checker is drawn and replaced before the second checker is drawn, the outcomes are independent. This means that the result of the first draw has no influence on the result of the second draw.
To calculate the probability of drawing a red checker both times, we need to multiply the probabilities of each individual draw.
The probability of drawing a red checker on the first draw is given by the ratio of the number of red checkers to the total number of checkers in the bag: 7 red / (7 red + 11 black) = 7/18.
Since the first draw is replaced before the second draw, the probabilities remain the same. Therefore, the probability of drawing a red checker on the second draw is also 7/18.
To calculate the total probability of drawing a red checker both times, we multiply the probability of each individual draw: (7/18) * (7/18) = 49/324.
So, the probability of drawing a red checker both times is 49/324.