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Chapter 5: Q 1.1. The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations (page 303)
Explain why events A and B are mutually exclusive
Because , A and B are mutually exclusive.
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Rolling dice Suppose you roll two fair, six-sided dice鈥攐ne red and one green. Are the events 鈥渟um is 8鈥� and 鈥済reen die shows a 4鈥� independent? Justify
your answer.
Recycling Do most teens recycle? To find out, an AP Statistics class asked an SRS of 100 students at their school whether they regularly recycle. How many students in the sample would need to say 鈥淵es鈥� to provide convincing evidence that more than half of the students at the school recycle? The Fathom dot plot below shows the results of taking 200 SRSs of 100 students from a population in which the true proportion who recycle is 0.50.
(a) Suppose 55 students in the class鈥檚 sample say 鈥淵es.鈥� Explain why this result does not give convincing evidence that more than half of the school鈥檚 students recycle.
(b) Suppose 63 students in the class鈥檚 sample say 鈥淵es.鈥� Explain why this result gives strong evidence that a majority of the school鈥檚 students recycle.
Education among young adults Chooses a young adult (aged to ) at random. The probability is that the person chosen did not complete high school, that the person has a high school diploma but no further education, and that the person has at least a bachelor鈥檚 degree.
(a) What must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor鈥檚 degree? Why?
(b) What is the probability that a randomly chosen young adult has at least a high school education? Which rule of probability did you use to find the
answer?
Role-playing games Computer games in which the players take the roles of characters are very popular. They go back to earlier tabletop games such as Dungeons & Dragons. These games use many different types of dice. A four-sided die has faces with and spots.
(a) List the sample space for rolling the die twice (spots showing on first and second rolls).
(b) What is the assignment of probabilities to outcomes in this sample space? Assume that the die is perfectly balanced.
Nickels falling over You may feel it鈥檚 obvious that the probability of a head tossing a coin is aboutbecause the coin has two faces. Such opinions are not always correct. Stand a nickel on the edge on a hard, flat surface. Pound the surface with your hand so that the nickel falls over. Do this time, and record the results.
(a) What鈥檚 your estimate for the probability that the
coin falls heads up? Why?
(b) Explain how you could get an even better estimate.
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