Suppose that you are offered the following “deal”. You roll a die. If you roll a 1, you win $15. If you roll a 2, 3, or 4 you win $10. If you roll a 5, or 6, you pay $20. A. Complete the PDF Table. List the x values from largest to smallest. x P(x) [ Select ] ["1", "3", "15"] [ Select ] ["1", "0.5", "0.17"] [ Select ] ["3", "2", "10", "4"] [ Select ] ["1", "0.17", "0.5"] [ Select ] ["6", "5", "20", "-20"] [ Select ] ["0.5", "2", "0.17", "0.33"]
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose that you are offered the following “deal”. You roll a die. If you roll a 1, you win $15. If you roll a 2, 3, or 4 you win $10. If you roll a 5, or 6, you pay $20.
A. Complete the
| x | P(x) |
| [ Select ] ["1", "3", "15"] | [ Select ] ["1", "0.5", "0.17"] |
| [ Select ] ["3", "2", "10", "4"] | [ Select ] ["1", "0.17", "0.5"] |
| [ Select ] ["6", "5", "20", "-20"] | [ Select ] ["0.5", "2", "0.17", "0.33"] |
B. Find the expected value. [ Select ] ["1.34", "1.07", "-0.19", "0.95"]
C. Interpret the expected value. [ Select ] ["You will win this much if you play a game.", "This is the most likely amount of money you will win.", "If you play many games you will likely win on average very close to this amount."]
D. Based on the expected value, should you play this game? [ Select ] ["Yes. The expected value is positive. If you play many games you are very likely to end up winning more money than you lose.", "No, the amount you lose is $20 which is more than any amount that you can win.", "No, this is a gambling game and it is always a bad idea to gamble."]
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