Homework 11: Suppose A Researcher Is Interested In The Numbe

Homework 11 Suppose A Researcher Is Interested In The Number Of Good

Suppose a researcher is interested in the number of good versus bad dreams that students have during final exam week. The researcher states that p = 0.68 that a student will have a bad dream during final exam week. Assuming complementary outcomes, what is the probability (q) that a student will have a good dream? q =

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In the context of probability theory, when analyzing outcomes that are mutually exclusive and collectively exhaustive, the sum of the probabilities of the outcomes equals 1. Here, the researcher indicates that the probability a student will have a bad dream during final exam week is p = 0.68. Since bad dreams and good dreams are complementary events—meaning one occurs if and only if the other does—their probabilities must sum to 1. Therefore, the probability q that a student will have a good dream can be calculated as follows:

q = 1 - p

Substituting the given value:

q = 1 - 0.68

q = 0.32

Hence, the probability that a student will have a good dream during final exam week is 0.32. This reflects the fundamental principle of complementarity in probability, illustrating how knowing the probability of one outcome directly informs the probability of its complement. This derivation underscores the importance of understanding basic probability concepts when assessing the likelihood of mutually exclusive events. Recognizing the complementarity allows researchers and analysts to efficiently calculate the probabilities of outcomes that are mutually exclusive, streamlining data analysis in psychological and behavioral studies such as dreams during stressful periods like final exams.

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