determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 5 red pieces of candy out of 55 pieces of candy total.
The two individual events are:
1. Randomly drawing a red piece of candy from the bag
2. Immediately eating the first red piece of candy and then randomly drawing another red piece of candy from the bag
These events are dependent because the outcome of the first event (drawing a red piece of candy) affects the probability of the second event (drawing another red piece of candy).
To find the probability of the combined event, we first calculate the probability of each event separately.
1. Probability of randomly drawing a red piece of candy:
There are 5 red pieces of candy out of a total of 55 pieces. Therefore, the probability of drawing a red piece of candy on the first draw is 5/55.
2. Probability of drawing another red piece of candy after eating the first one:
After eating the first red candy, there are now 4 red pieces of candy left out of a total of 54 pieces. Therefore, the probability of drawing another red piece of candy on the second draw is 4/54.
To find the probability of the combined event (drawing and immediately eating two red pieces of candy in a row), we multiply the probabilities of the individual events:
Probability = (5/55) * (4/54) = 20/2970
Therefore, the probability of the combined event is 20/2970.