Using Probabilities for Significant Events

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Question

Using Probabilities for Significant Events

c. Which probability is relevant for determining whether 1 is a significantly low number of matches: the result from part (a) or part (b)?

Accepted Answer

All right, hello, everyone. So this question says, a game involves selecting 3 digits from 0 to 9 with repetition allowed. The random variable Y represents the number of digits that match the winning numbers in the exact order. Assume that the probability of getting one or fewer matches, that is of Y is less than or equal to 1, is 0.972. And the probability of getting exactly one match, that is Y equals 1, is 0.243. Which probability is relevant for determining whether one match is a significantly low number? And here we have 4 different answer choices labeled A through D. A says the probability of getting exactly 1 match. B says probability of getting one or fewer matches, C says none, and D says both. All right, so first and foremost, what does it mean for a probability to be considered a significantly low number? Recall that in statistics we use that phrase to describe if an observed outcome is unusually small compared to what you would expect to see. So, to be precise, right, a number or an outcome rather, is considered significantly low when the probability of either that outcome. Or of anything lower is typically. 5% or less. So it's 0.05 or less. This is known as the left tail probability, and it's used to measure how rare small values are. So to put this in a different perspective. When evaluating if one match is significantly low, it's not that we just look at. The probability of getting precisely one match. Instead, we look at the probability of getting either one match or less than that. So in this case, we would look at the probability where Y is less than or equal to 1. And if that value is 5% or less, then we can conclude that the probability of getting one match is significantly low. So in this particular case, The probability of getting either one match or no matches just so happens to be 0.972. So here, because the value is not less than 0.05, it's not considered significantly low. And therefore Right. Our correct answer is going to be option B in the multiple choice, because it's the probability of getting one or fewer matches that would help us determine if the probability of one match is significantly low or not. And in this case, it's not significantly low. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

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Using Probabilities for Significant Events

c. Which probability is relevant for determining whether 1 is a significantly low number of matches: the result from part (a) or part (b)?

Key Concepts

Probability Distribution

Significance Level

Hypothesis Testing

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Using Probabilities for Significant Eventsc. Which probability is relevant for determining whether 1 is a significantly low number of matches: the result from part (a) or part (b)?