"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
28. Blood Types The probability that a Latinx American person in the United States has type A+ blood is 29%. Four Latinx American people in the United States are selected at random. (Source: American National Red Cross)
a. Find the probability that all four have type A+ blood."

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability that all four Latinx American people selected at random have type A+ blood. This involves using the Multiplication Rule for independent events.
2. Step 2: Recall the Multiplication Rule. The rule states that if events are independent, the probability of all events occurring is the product of their individual probabilities. Mathematically, this can be expressed as: $P(A\; \backslash (\backslash cap\backslash )\; B\; \backslash (\backslash cap\backslash )\; C\; \backslash (\backslash cap\backslash )\; D)\; =\; P(A)\; \backslash (\backslash cdot\backslash )\; P(B)\; \backslash (\backslash cdot\backslash )\; P(C)\; \backslash (\backslash cdot\backslash )\; P(D)$.
3. Step 3: Identify the probability of a single event. From the problem, the probability that one Latinx American person has type A+ blood is 29%, or $P(A)\; =\; 0.29$.
4. Step 4: Apply the Multiplication Rule. Since the selection of each person is independent, the probability that all four have type A+ blood is: $P(A\; \backslash (\backslash cap\backslash )\; B\; \backslash (\backslash cap\backslash )\; C\; \backslash (\backslash cap\backslash )\; D)\; =\; P(A)\; \backslash (\backslash cdot\backslash )\; P(A)\; \backslash (\backslash cdot\backslash )\; P(A)\; \backslash (\backslash cdot\backslash )\; P(A)\; =\; (P(A))^4$.
5. Step 5: Substitute the probability value into the formula. Replace $P(A)$ with 0.29 to get: $(0.29)^4$. This is the probability that all four selected individuals have type A+ blood.

Key Concepts

Multiplication Rule of Probability

The Multiplication Rule states that the probability of two or more independent events occurring together is the product of their individual probabilities. In this context, if the probability of one person having type A+ blood is 29%, the probability of four independent individuals all having type A+ blood is calculated by multiplying 0.29 by itself four times.

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, the selection of one Latinx American person does not influence the blood type of another. This independence allows us to apply the Multiplication Rule effectively, as the probability remains constant across each selection.

Probability Calculation

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. To find the probability that all four selected individuals have type A+ blood, we calculate it as (0.29)^4, which quantifies the chance of this specific outcome happening in a random selection of four people.