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Die, Card and Cash in Hand Game Probabilities

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One fair die is rolled. What is the probability of getting an even number?

A card is selected at random from an ordinary 52-card deck. What is the probability that it is a heart?

In the Maryland Cash In Hand game, to win the grand prize the contestant must match seven distinct numbers, in any order, among the numbers 1 through 31 randomly drawn by a lottery representative. What is the probability of choosing the winning numbers?

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Solution Summary

Brief calculations are given to find basic probabilities in games of chance for 3 questions.

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One fair die is rolled. What is the probability of getting an even number?

When a fair die is rolled, there are 6 outcomes: 1,2,3,4,5,6. As 2,4, or 6 are even, the probability of getting an even number is
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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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