MATH 214 Midterm: MATH214_ALL-SECTIONS_SPRING2012_0000_MID_EXAM_1
10 Jan 2019
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Math 214 Exam 2 Spring 2012
Instructions: This exam consists of eight questions, found on the front and back of this page. Solve each
problem on the indicated answer sheet. Round decimal answers to three decimal places where necessary, or
leave answers as exact fractions. Calculators are allowed but you must show calculations for full credit. No
other aids are permitted.
Answer questions 1 - 3 on Answer Sheet 1.
1) At the local auto inspection station, 25% of all cars fail the emissions inspection and 12% of all cars fail the
safety inspection. 8% of cars fail both inspections.
a) If one car is chosen at random, what is the probability that it passes both inspections? [5 pt]
b) If a randomly chosen car fails the emissions inspection, what is the probability that it also fails the safety
inspection? [5 pt]
c) For a randomly chosen car, are the events “fails emissions inspection” and “fails safety inspection”
independent? Justify your answer with a calculation. [5 pt]
d) If four cars are chosen at random, what is the probability that all four pass the safety inspection? [5 pt]
e) If four cars are chosen at random, what is the probability that they do not all fail the emissions
inspection? [5 pt]
2) Stacy is up to bat in a softball game. If the first pitch is a strike, the probability is .32 that she will ultimately
strike out. If the first pitch is not a strike, then the probability is only .13 that she will strike out. The pitcher
Stacy is currently facing throws a first-pitch strike 62% of the time. What is the probability that Stacy will strike
out this time? [5 pt]
3) Determine whether the game described below is fair, by calculating each player’s probability of scoring a
point. Show the analysis that leads to your conclusion. [6 pt]
“Dice War” is a three-player game. For each round, two standard six-sided dice are rolled. If the sum is 4, 5, or
6, Player A scores a point. If the sum is 8, 9, or 10, Player B scores a point. Otherwise Player C scores a point.
The winner is the player with the most points after 20 rounds.”
Answer questions 4 - 5 on Answer Sheet 2.
4) As a prize for a school carnival, Wendell is allowed to take one bill at random from one of two bags of
money. The first bag contains one $10 bill and three $1 bills. The second bag contains three $10 bills and
twelve $1 bills.
a) From which bag should he decide to pick his money, and why? [5 pt]
b) Explain (briefly) the common misconception that could lead Wendell to decide on the wrong bag. [5 pt]
5) You pick two marbles at random from a bag containing 1 red, 5 blue, and 9 green marbles.
a) Write down the sample space for this experiment. [4 pt]
b) Find the probability that you choose at least one green marble. [4 pt]
c) Find the probability that you choose exactly one green marble. [4 pt]
Document Summary
Instructions: this exam consists of eight questions, found on the front and back of this page. Solve each problem on the indicated answer sheet. Round decimal answers to three decimal places where necessary, or leave answers as exact fractions. Calculators are allowed but you must show calculations for full credit. Answer questions 1 - 3 on answer sheet 1: at the local auto inspection station, 25% of all cars fail the emissions inspection and 12% of all cars fail the safety inspection. [5 pt: stacy is up to bat in a softball game. If the first pitch is a strike, the probability is . 32 that she will ultimately strike out. If the first pitch is not a strike, then the probability is only . 13 that she will strike out. Stacy is currently facing throws a first-pitch strike 62% of the time. [5 pt: determine whether the game described below is fair, by calculating each player"s probability of scoring a point.
