Would you please help/check my answers on these probability questions because I cannot come up with what the answer book says.
A group of baseball fans at a sports bar in Illinois were asked about which professional baseball team they root for during baseball season. Use the results in the table to answer each question.
Team Number of Fans
Cubs 14
Cardinals 42
White Sox 25
a. What is the probability that a randomly selected fan is not a Cubs fan?
I said .83 because non-cubs fans are 42+25=67/81 = .83.
The answer book says .74
b. Suppose a new fan walked into the room and didn't really like baseball but wanted to play along, so she agreed to randomly select one of the three teams. What is the probability that she is a Cardinals fan?
I said .33 because she has a chance to pick Cardinals out of the three teams, 1/3 = .33
Agrees with answer book.
c. If one fan is chosen randomly, what is the probability that he or she roots for the White Sox?
I said .31 because 25/81 = .81, however, the answer book says .22 and I can't figure out how they got that.
Thank you so much for checking.
I completely agree with you. My only thought is that there are typos in the book. Your typo:
25/81 ≠ .81
Could someone else please look at this? I did not say that 25/81 was .81 and I'd also like to check my other answers. Thanks!
Let's go through each question step by step:
a. What is the probability that a randomly selected fan is not a Cubs fan?
To find the probability that a randomly selected fan is not a Cubs fan, we need to calculate the number of non-Cubs fans divided by the total number of fans. In this case, there are 42 Cardinals fans and 25 White Sox fans, making a total of 67 non-Cubs fans. Since the total number of fans is 14 + 42 + 25 = 81, the probability is 67/81 ≈ 0.827.
Therefore, your answer of 0.83 is correct, not the one given in the answer book.
b. Suppose a new fan walked into the room and didn't really like baseball but wanted to play along, so she agreed to randomly select one of the three teams. What is the probability that she is a Cardinals fan?
Since the new fan is randomly selecting one of the three teams, each team has an equal chance of being selected. Therefore, the probability of selecting the Cardinals is 1/3 = 0.333.
Your answer of 0.33 is correct, matching the answer book.
c. If one fan is chosen randomly, what is the probability that he or she roots for the White Sox?
To find the probability that a randomly selected fan roots for the White Sox, we need to calculate the number of White Sox fans divided by the total number of fans. In this case, there are 25 White Sox fans out of the total 81 fans. So, the probability is 25/81 ≈ 0.309.
Your answer of 0.31 is very close, but the answer book rounded it to 0.22 for some reason. Please double-check if there was any additional information provided in the question or if there is any explanation offered for the answer book's response.
In conclusion, your answers for questions a and b are correct, while your answer for question c is very close to the correct value, but it seems there might be an error in the answer book or additional information missing in the question for that specific answer.
Let's go through each question and see where the discrepancies might be:
a. What is the probability that a randomly selected fan is not a Cubs fan?
Your initial calculation of (42 + 25) / 81 = 67 / 81 = 0.83 is correct. This is the probability of selecting a non-Cubs fan from the total number of fans. Therefore, your answer of 0.83 is correct, and it seems the answer book is incorrect.
b. Suppose a new fan walked into the room and didn't really like baseball but wanted to play along, so she agreed to randomly select one of the three teams. What is the probability that she is a Cardinals fan?
Since there are three teams and she is randomly selecting one, the probability of her choosing the Cardinals is indeed 1/3 or 0.33. Your answer matches with the answer book, so that is correct.
c. If one fan is chosen randomly, what is the probability that he or she roots for the White Sox?
In this case, you calculated 25/81 = 0.31. However, this is not the correct calculation based on the information provided in the table. To calculate the probability, you need to divide the number of White Sox fans by the total number of fans, which is 14 + 42 + 25 = 81. Therefore, the correct calculation is 25 / 81 = 0.31. Your answer is correct, and it seems the answer book is incorrect in this case as well.
So, in summary:
a. Your answer of 0.83 is correct.
b. Your answer of 0.33 is correct.
c. Your answer of 0.31 is correct.
It seems that there might be errors in the answer book. It's always a good practice to double-check your answers and calculations, and in this case, your calculations are indeed correct.