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Finding a probability based on a table

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1. How many ways can 15 girls be chosen to form a baseball team (need 9 players)?

5005
1,816,214,400
24
135

3. Use this table to answer questions #3 through #6. Some students were asked if they carry a credit card. Here are the responses.
Class______ | Credit Card Carrier | Not a Credit Card Carrier | Total
Freshman______________33_______________________27________________60
Sophomore______________6_______________________34________________40
Total__________________39_______________________61________________100
What is the probability that the student didn't carry a credit card?

4. What is the probability that the student is a freshman and carries a credit card?

5. What is the probability that the student is a sophomore given he doesn't carry a credit card?

6. Are Credit Card Carriers and Freshmen independent events? Prove this mathematically

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This solution contains a detailed explanation of finding a probability based on a table.

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1. How many ways can 15 girls be chosen to form a baseball team (need 9 players)?

5005
1,816,214,400
24
135

Solution. The number ways is
C(15, 9)=15!/[9!*6!]=5005

So, the first answer is correct.

3. Use this table to answer questions #3 through #6. Some students were asked if they carry a credit card. Here are the responses.
Class______ | Credit Card Carrier | Not a Credit Card Carrier | ...

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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!"
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