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

c. Find the probability of randomly selecting three different people and finding that all of them have blue eyes.

검증된 단계별 안내

Step 1: Understand the problem. The probability of a single person having blue eyes is given as 35%, or 0.35. We are tasked with finding the probability that all three randomly selected people have blue eyes.

Step 2: Recognize that this is a problem involving independent events. The probability of all three people having blue eyes can be calculated by multiplying the probabilities of each individual event, since the selection of one person does not affect the others.

Step 3: Write the formula for the probability of all three events occurring. This can be expressed as: P(All three have blue eyes) = P(Person 1 has blue eyes) × P(Person 2 has blue eyes) × P(Person 3 has blue eyes).

Step 4: Substitute the given probability (0.35) into the formula. This becomes: P(All three have blue eyes) = 0.35 × 0.35 × 0.35.

Step 5: Simplify the expression by multiplying the probabilities together. This will give the final probability of all three people having blue eyes.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 selecting individuals with blue eyes from a population where 35% have this trait. The probability of independent events can be calculated by multiplying the probabilities of each event occurring.

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, selecting one person with blue eyes does not influence the likelihood of the next person also having blue eyes. This property allows us to multiply the probabilities of each selection to find the overall probability of all selected individuals having blue eyes.

Binomial Probability

Binomial probability refers to the probability of obtaining a fixed number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. In this case, we can use the binomial formula to calculate the probability of selecting three people, all of whom have blue eyes, given the probability of any one person having blue eyes is 0.35.

Blue Eyes Assume that 35% of us have blue eyes (based on a study by Dr. P. Soria at Indiana University).c. Find the probability of randomly selecting three different people and finding that all of them have blue eyes.