Question

consider the following fallacy explain why the fallacy applies to the example and create your own argument that displays the same fallacy. the gamblers fallacy has the following form. premise x has been happening more than it should. conclusion: x will come to an end soon. example it has rained for 10 days, which is unusual around here. tomorrow will be sunny. a. let x be that it is sunny. this argument claims that x has been occurring more than it should, so it will come to an end soon. b. let x be that it rained on a day. this argument claims that x has been occurring more than it should, so the claim that x is unusual is false. c. let x be that it is sunny. this argument claims that x has been occurring more than it should, so the claim that x is unusual is false. d. let x be that it rained on a day. this argument claims that x has been occurring more than it should, so it will come to an end soon. create an argument that displays the same fallacy. choose the correct answer below. a. a basketball team has missed 27 3 - point field goal attempts in a row. they will make their next 3 - pointer. b. a soccer goalie has stopped the last 20 shots on goal. they will also be successful in stopping the next shot. c. you flipped a coin 10 times and it came up tails every time. the coin may not be a fair coin. d. you rolled a six - sided die six times but did not roll a 5. the probability of rolling a 5 is still 1 in 6.

Explanation:

• For the first part: In the example, \(X\) is "it rained on a day". It has rained for 10 days (more than usual), and the conclusion is that \(X\) (rain) will come to an end (tomorrow will be sunny). So, we check each option. Option A and C have \(X\) as "it is sunny" which is wrong. Option B has the wrong conclusion (claiming \(X\) is not unusual is false instead of \(X\) will end). Option D is correct as \(X\) is "it rained on a day" and the conclusion is \(X\) will end soon.
• For the second part: The gambler's fallacy is thinking that because an event has occurred more than expected, it will stop. In option A, a basketball team has missed 27 3 - point field goals (more than expected), and the conclusion is they will make the next one (the streak of misses will end). Option B is expecting a streak to continue (not the fallacy). Option C is about the fairness of the coin (not the fallacy). Option D is a correct probability statement (not the fallacy).

Answer:

• First part: D. Let \(X\) be that it rained on a day. This argument claims that \(X\) has been occurring more than it should, so it will come to an end soon.
• Second part: A. A basketball team has missed 27 3 - point field goal attempts in a row. They will make their next 3 - pointer.