# Worksheet 7

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WORKSHEET 7 1. A card is selected at random from a pack consisting of a total of 52 cards, including 4 queens and 4 kings. The card is not replaced. A second card is selected. Find the probability that the second card is a queen, given that the first card is a king. (A standard deck has a total of 52 cards, including 4 queens and 4 kings as shown in the lecture notes) 2. A Statistics class has an enrollment of 300. Out of these, 95 are taking the Actuarial Statistics major, 120 are Data Science majors, 80 are Financial Math majors and 5 are Undecided. Find the probability that a student in the class chosen at random is neither an Actuarial Statistics nor a Data Science major. 3. A two-digit number is chosen at random. What is the probability that the chosen number is a multiple of 5? 4. Next quarter, a student must choose 4 courses among the 20 being offered. In order to complete his major requirements, at least one of these courses must be from the PSTAT department, which is offering 5 courses. How many ways can he choose the 4 courses? (Hint: the answer is NOT ( 5 1 )( 19 3 ) . Consider counting the number of invalid selections). 5. Three white paint balls, A, B and C, are fired at a target independently. The probability that paint ball A will hit the target is 0.7, the probability that paint ball B will hit the target is 0.8, and the probability that paint ball C will hit the target is 0.9. a. What is the probability that at least one of them will hit the target? b. What is the probability that A will miss, B will hit the target and C will miss the target? 6. Among 35 students in a class, 17 earned "A" on the midterm, 14 earned "A" on final exam, and 11 did not earn "A" on either exam. What is the probability that a randomly selected student from this class earned "A" on both exams? END WORKSHEET 7