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Answer :
Final answer:
The question involves calculation and understanding of probability in relation to a Binomial distribution. The probability of finding an extra fortune in 144 fortune cookies is .03 leading to an expected 4.32 fortunate cookies with extra fortunes. The increasing number of trials sees a convergence of probabilities.
Explanation:
The question relates to the concept of probability distribution in mathematics. Specifically, it involves calculation of probability as well as understanding the binomial distribution and Poisson distribution.
From the information given, X represents the number of fortune cookies that contain an extra fortune where X follows a Binomial distribution, as depicted by X~ B(144, .03). This suggests that we are dealing with 144 trials (fortune cookies) each with a probability of success (finding an extra fortune) of 0.03. So, the expected number of successes, denoted by 'd', is 144 multiplied by 0.03, which equals 4.32 cookies. However, only the values 0, 1, 2, 3,... 144 are possible.
Moreover, the question indicates that as the number of trials (n) increases, the probabilities get closer together. This is characteristic of both Binomial and Poisson distributions but since the problem instructs us to use only one distribution to solve, the one used here is binomial which is best suited for a fixed number of trials.
Learn more about Probability Distribution here:
https://brainly.com/question/14210034
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