Cynthia has a bag of jellybeans. There are two red jellybeans, one yellow jellybean, and two black jellybeans in her bag. Cynthia grabs two jellybeans and gives them to her friend, Pedro, and he eats them. What is the probability that she gives him two red jellybeans?
This is a dependent event because Cynthia is putting the jellybeans back into the bag.
To find the probability that Cynthia gives Pedro two red jellybeans, we need to calculate the probability of two events happening in succession: Cynthia selecting a red jellybean on her first draw and then selecting another red jellybean on her second draw.
Step 1: Calculate the probability of selecting a red jellybean on the first draw
Out of the total number of jellybeans in the bag (5), there are 2 red jellybeans. Therefore, the probability of Cynthia choosing a red jellybean on the first draw is 2/5.
Step 2: Calculate the probability of selecting a red jellybean on the second draw, given that a red jellybean was selected on the first draw
Since the jellybean is not replaced after the first draw, the total number of jellybeans decreases by 1 for the second draw. After one red jellybean has been selected and removed, there is only 1 red jellybean left in the bag. The total number of jellybeans remaining is 4. Therefore, the probability of selecting a red jellybean on the second draw, given that a red jellybean was selected on the first draw, is 1/4.
Step 3: Calculate the probability of both events happening in succession
To find the probability of two independent events happening in succession, we multiply the probabilities of each event. Therefore, the probability of Cynthia giving Pedro two red jellybeans is (2/5) * (1/4) = 1/10.
So, the probability that Cynthia gives Pedro two red jellybeans is 1/10.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
2/5 * (2-1)/(5-1) = ?