Bobby has a bag of marbles with nine red marbles, 13 yellow marbles and six orange marbles. He picks one marble and keeps it out. He wants to find the probability of picking a yellow marble by randomly picking one more marble from the bag. What type of event does this situation represent?
probability, ratio etc
This situation represents a dependent event.
A dependent event is an event where the outcome of one event affects the probability of the outcome of another event. In this case, Bobby picking one marble from the bag and keeping it out will affect the probability of picking a yellow marble on the second pick. Since one marble has already been removed from the bag, the total number of marbles and the composition of the marbles in the bag has changed, which in turn affects the probabilities.
To calculate the probability of picking a yellow marble on the second pick, we need to consider the new composition of the bag after the first marble is removed.
Initially, the bag contains 28 marbles (9 red + 13 yellow + 6 orange). After removing one marble, there are 27 marbles remaining in the bag. Of these, there are still 13 yellow marbles.
Therefore, the probability of picking a yellow marble on the second pick can be calculated as the number of favorable outcomes (picking a yellow marble) divided by the number of possible outcomes (remaining marbles):
Probability = Number of yellow marbles / Number of remaining marbles
= 13 / 27
≈ 0.481 or 48.1%