You select a family with three children. If M represents a...

You select a family with three children. If $M$ represents a male child and $F$ a female child, the sample space of equally likely outcomes is $\{M M M, M M F, M F M, M F F, F M M FMF, FFM, FFF$} - Find the probability of selecting a family with $$\text{at least two female children.}$$

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Key Concepts

Counting Techniques/Combinatorics

Counting techniques, including listing outcomes and using combinatorial formulas, are essential for accurately determining the number of favorable outcomes. These techniques are especially useful in problems that require counting outcomes that satisfy certain conditions.

Classical Probability Calculation

Classical probability involves determining the probability of an event by dividing the count of favorable outcomes by the total number of outcomes in the sample space. This method is effective when all outcomes are equally likely.

At Least Concept

The 'at least' concept in probability specifies that the desired event includes a minimum number of occurrences. It requires considering all outcomes where the condition is met or exceeded, often involving summing counts across multiple cases.

Sample Space

A sample space is the set of all possible outcomes of an experiment or random event. It provides the complete context for the experiment, allowing for the systematic assignment of probabilities to events.

Equally Likely Outcomes

Equally likely outcomes are those where each outcome in the sample space has the same probability of occurring. This assumption simplifies probability calculations by enabling the use of ratios of counts of outcomes.

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