Find the probability for the experiment of drawing two...

Find the probability for the experiment of drawing two marbles at random (without replacement) from a bag containing one green, two yellow, and three red marbles. (Hint: Use combinations to find the numbers of outcomes for the given event and sample space.)
Both marbles are yellow.

Key Concepts

Probability

Probability is the measure of how likely an event is to occur. It is calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space. This concept is fundamental in assessing risk and uncertainty in various experiments and real-world situations.

Sample Space

The sample space is the set of all possible outcomes of an experiment. In probability problems, determining the sample space is essential because it provides the denominator in the probability fraction, representing every potential outcome that could occur.

Combinations

Combinations are a counting technique used to determine the number of ways to select items from a larger set when the order of selection does not matter. This concept is particularly important in probability problems involving selection without replacement, where the sequence of choices is irrelevant.

Favorable Outcome

A favorable outcome refers to any outcome that meets the criteria set by the event of interest. In probability calculations, counting the number of favorable outcomes allows for the calculation of the event's probability by comparing it to the total number of outcomes in the sample space.

Without Replacement

Drawing without replacement means that once an item is selected, it is not returned to the original set for subsequent selections. This concept is key in probability problems because it affects the composition of the sample space and the independence of events, often leading to dependent probabilities.

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