Introductory Statistics, Quiz 3 Solutions

Quiz 3 For questions 1-5: You have a deck of cards (52 cards: 4 suits: hearts, spades, diamonds, and clubs, and 2,3,4,5,6,7,8,9,10,J,Q,K,A for each suit). You don’t need to simplify the fractions. 1. If you select one card randomly, what is the probability that it will be the ace of hearts? 1/52 2. If you select one card randomly, what is the probability that it will be a diamond or a club? 13/52+ 13/52 = ½ 3. If you select one card randomly, what is the probability that it will be a diamond or a king? 13/52 + 4/52 – 1/52 = 16/52 4. If you select two cards randomly with replacement, what is the probability that both of them will be a 10? (4/52)(4/52) 5. If you select two cards randomly without replacement, what is the probability that both of them will be a 10? (4/52)(3/51) 6. Write the sample space: A coin is flipped and a die is rolled at the same time. S = {T1, T2, T3, T4, T5, T6, H1, H2, H3, H4, H5, H6} What is the probability that the coin shows Tail and the dice shows an odd number? That is T1, T3, T5. So the probability is 3/ 12. 7. A multiple choice quiz has 5 questions with four choices for each question. If a student just guesses all the answers, what is the probability that the student will get a 100% on the quiz? (1/4)(1/4) (1/4) (1/4) (1/4) = (1/4)5 8. The probability distribution of a certain medical condition and the results of the medical test are given below. Use the table to answer the questions below. Have condition Test positive 998 Test negative 2 Total 1000 Don’t have condition 1,998 997,002 999,000 Total 2,996 997,004 1,000,000 a. What is the probability that a randomly selected person has the condition? 1000/1,000,000 b. What is the probability that a randomly selected person tested positive? 2996/1,000,000 c. What is the probability that a person will be tested positive given he/she doesn’t have the condition? 1998/999,000 d. What is the probability that a person has the condition given he/she tested positive? 998/2996 e. What is the probability that a person will be tested negative, given he/she has the condition? 2/1000 9. In a certain bank, previous records show that out of all prospective customers walking into the bank, 60 % open a checking account, 25% open a savings account and 15% open both accounts. Suppose a prospective customer is picked at random. What is the probability that this prospective customer will open a checking account OR a savings account? P(checking or savings) = P(checking) + P(savings) – P(checking and savings) \ P(checking or savings) = 60% + 25% -15% = 70% 10. Suppose that a sample space S consists of four simple events: A, B, C, and D. That is S = {A, B, C, D}. If P(A) =0.4, P(B) = 0.1, P(C) = 0.2, what is P(D)? Since the probabilities must add up to 1, P(D) = 1 – (0.4 + 0.1 + 0.2) = 0.3 11. A club with 50 members wants to elect a president, a vice-president, and a treasurer. How many possible way can they select these officers? Since order DOES matter here, it’s Permutation: 50P3 = 117,600 12. A club with 50 members wants to send a 5-member committee to the national meeting. How many ways can they select the members for the committee? Since order DOES NOT matter here, it’s Combination: 50C5 = 2,118,760 How many ways can the letters of ADDITIONALLY be arranged? 13. ଵଶ! ଶ!ଶ!ଶ!ଶ! 14. =29,937,600 Determine whether the given procedure results in a binomial distribution. For those that are not binomial, identify at least one requirement that is not satisfied. • Determining whether each of 3000 heart pacemakers is acceptable or defective. Binomial. • Recording the number of children in 300 families. Not binomial: there are more than two outcomes.