STA 2023 Spring 2011 Exam 2 sample

Assume that the trials are independent in the following questions.

Question 1 – 4:A survey asking,“Do you favor gun control?” produces the following contingency table:

Male / Female
Yes / 23 / 36
No / 56 / 44

One person is selected at random. Find the probability that the person chosen

  1. was a male:
  1. was a female and responded ‘yes’:
  1. was a male, or responded ‘no’:
  1. was a female, given that the person responded ‘no’:
  1. A fair coin is flipped 3 times. What is the probability of obtaining heads no more than twice?
  1. A fair coin is flipped 5 times. What is the probability of obtaining tails at least once?

Question 7 – 9: A fair die is rolled twice. Find the probability of obtaining

  1. two odd numbers:
  1. a sum of 8:
  1. a sum of 8, given that you have two odd numbers:

Question 10 – 12: Let X be the number of books borrowed by a student at the library. The past data shows the probability distribution.

x / P(x)
0 / 0.12
1 / 0.32
2 / 0.28
3 / ?
  1. What is the probability that exactly 3booksare borrowed by a student?
  1. What is the probability thatmore than1book isborrowed by a student?
  1. What is the expected number of booksborrowed by a student?(round to 1-decimal)

Question 13 – 15: A fair die is rolled once.

  1. What is the probability of obtaining a number that is even or greater than 4?
  1. What is the probability of obtaining a number that is odd and smaller than 5?
  1. What is the probability of obtaining a number that is larger than 2, given that it’s odd?
  1. When you give a casino $5 for a bet on the number 7 in roulette, you have a 1/38 probability of winning $175. What is your expected profit? (round to 2-decimals) --- answer: -0.26
  1. In Illinois’ Pick 3 lottery game, you pay $1 to select a sequence of 3 digits, such as 011. If you win by selecting the same sequence that is drawn, you collect $300. Find the expected profit. (round to 1-decimal) --- answer: - 0.7
  1. At a Florida college, 22% of students speak Spanish, 5% speak French, and 3% speak both languages. What is the probability that a student chosen at random from the college speaks neither Spanish nor French?

Question 19 – 21: Past data reveals that the graduation rate was 72% for the medical school at a university. If 10 medical students are randomly selected from that school,

  1. Find the probability that only 4 of them will graduate. (round to 3-decimals)

A) 0.000 B) 0.035 C) 0.180 D) 0.027 E) None of these

  1. Find the probability that at most one of them will graduate.(round to 3-decimals)

A) 0.000 B) 1.000 C) 0.180 D) 0.027 E) None of these

  1. Find the expected number of students who graduate in such a group of 10.

A) 7.2 B) 72 C) 2.8 D) 28 E) 10

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