What is the probability that at least one of the kindergarten students will be immunized?

Rationale

1 - (0.35)^6 represents the probability that at least one of the kindergarten students will be immunized.

To find the probability that at least one student is immunized, we can use the complement rule. First, we calculate the probability that none of the students are immunized, which is given by (0.35)^6, and then subtract this value from 1.

A (0.65) YOUR ANSWER

This choice represents the probability that a single student is immunized. However, the question asks for the probability that at least one student out of multiple students is immunized, which requires a different calculation involving the collective probability.

B (1 - (0.65)^6) YOUR ANSWER

This option incorrectly uses the probability of a single student being immunized (0.65) to find the probability that at least one is immunized among six students. Instead, the correct approach is to first determine the probability of none being immunized (0.35) and then use the complement of that value.

C (0.35) YOUR ANSWER

This value indicates the probability that a single student is not immunized. Similar to option A, this choice does not address the situation of multiple students and does not lead to the correct calculation for at least one immunized student.

D (1 - (0.35)^6) CORRECT

This choice accurately reflects the probability that at least one of the six kindergarten students is immunized. It calculates the complement of the probability that none are immunized, making it the correct approach for this question.

Conclusion

The probability that at least one of the kindergarten students will be immunized is calculated using the complement of the probability that none are immunized. Hence, 1 - (0.35)^6 correctly captures this scenario, while the other options either reflect the probability for a single student or misapply the complement rule. Understanding these principles is crucial for accurately assessing probabilities in multiple trials.

What is the probability that at least one of the kindergarten students will be immunized?

1 - (0.35)^6 represents the probability that at least one of the kindergarten students will be immunized.

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