Women in Movies In a recent year, speaking characters in movies w...

4. Probability

Complements

Statistics

4. Probability

Complements

1:51 minutes

Problem 4.2.5

Textbook Question

Women in Movies In a recent year, speaking characters in movies were 68.2% male. What is the probability of randomly selecting a character with a speaking part and getting a female? What should be the value of that probability?

Verified step by step guidance

Step 1: Understand the problem. The problem states that 68.2% of speaking characters in movies are male. To find the probability of selecting a female character, we need to calculate the complement of the probability of selecting a male character.

Step 2: Recall the complement rule in probability. The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. Mathematically, this can be expressed as:

P(	ext{Female}) = 1 - P(	ext{Male})

Step 3: Substitute the given probability of selecting a male character into the formula. The problem states that

P(	ext{Male}) = 0.682

. Using the complement rule, substitute this value into the formula:

P(	ext{Female}) = 1 - 0.682

Step 4: Perform the subtraction to find the probability of selecting a female character. This step involves calculating

1 - 0.682

, which will give the probability of selecting a female character.

Step 5: Interpret the result. The resulting probability represents the likelihood of randomly selecting a speaking character in movies and getting a female. Ensure the final probability is expressed as a decimal or percentage, depending on the context.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it refers to the chance of randomly selecting a female character from a group of speaking characters in movies. The probability can be calculated by dividing the number of favorable outcomes (female characters) by the total number of possible outcomes (all speaking characters).

Complementary Events

Complementary events are pairs of outcomes that cover all possible scenarios of a given situation. In this case, the probability of selecting a female character is the complement of selecting a male character. Since 68.2% of speaking characters are male, the probability of selecting a female character can be found by subtracting the probability of selecting a male from 1, which highlights the relationship between these two outcomes.

Percentage to Probability Conversion

Converting percentages to probabilities is essential for statistical analysis. A percentage represents a part of a whole, while probability quantifies the chance of an event occurring. To find the probability of selecting a female character, one must first convert the percentage of male characters (68.2%) into a decimal (0.682) and then use this value to determine the probability of selecting a female character, which is 1 - 0.682.

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