Blue Eyes Assume that 35% of us have blue eyes (based on a study ...

4. Probability

Complements

Statistics

4. Probability

Complements

2:00 minutes

Problem 6.CRE.4

Textbook Question

Blue Eyes Assume that 35% of us have blue eyes (based on a study by Dr. P. Soria at Indiana University).

b. Find the value of P(B_bar).

Verified step by step guidance

Step 1: Understand the problem. The problem involves finding the complement probability of the event B, where B represents the event that a person has blue eyes. The complement of an event, denoted as B̅, represents the event that a person does NOT have blue eyes.

Step 2: Recall the complement rule in probability. The complement rule states that the probability of the complement of an event is given by: P(B̅) = 1 - P(B).

Step 3: Identify the given probability. From the problem, we are told that P(B) = 0.35, which is the probability that a person has blue eyes.

Step 4: Substitute the given value into the complement rule formula. Using the formula P(B̅) = 1 - P(B), substitute P(B) = 0.35 to calculate P(B̅).

Step 5: Simplify the expression. Perform the subtraction to find the value of P(B̅), which represents the probability that a person does NOT have blue eyes.

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Key Concepts

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

Complementary Probability

Complementary probability refers to the likelihood of an event not occurring. If the probability of an event A happening is P(A), then the probability of A not happening, denoted as P(A'), is calculated as P(A') = 1 - P(A). In this case, if 35% of people have blue eyes, the probability of not having blue eyes is the complement of this percentage.

Probability Notation

Probability notation is a standardized way to express the likelihood of events. In this context, P(B) represents the probability of event B occurring, while P(B_bar) or P(B') denotes the probability of event B not occurring. Understanding this notation is crucial for interpreting and solving probability problems accurately.

Basic Probability Calculation

Basic probability calculation involves determining the likelihood of an event based on known data. For example, if 35% of a population has blue eyes, the calculation for the probability of not having blue eyes (P(B_bar)) involves subtracting the given percentage from 100%. This fundamental skill is essential for solving various statistical problems.

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Blue Eyes Assume that 35% of us have blue eyes (based on a study by Dr. P. Soria at Indiana University).b. Find the value of P(B_bar).