Opening the book…
In the following exercises, decide whether the described experiments are binomial experiments. For those that are not, explain why they aren’t.
A golfer practices putts from 1 foot, 2 feet, 3 feet, 4 feet, and 5 feet; “success” is defined as making the putt.
A game designer rolls a pair of dice 100 times and counts the number of times the sum is at least 10.
A student who is completely unprepared for a multiple-choice pop quiz guesses on all 10 questions. There are 4 choices for each of the first 5 questions and 5 choices for each of the last 5 questions. “Success” is defined as answering the question correctly.
A baseball player is practicing pitching; he throws pitches until he gets 50 strikes.
A statistician stops 20 college students at random outside a dining hall and notes their class year.
An employee at a bowling alley watches each patron’s first ball and counts how many are strikes over the course of his shift.
In the following exercises, you have an 8-sided die with 4 faces colored orange, 3 colored red, and 1 colored yellow. You’re going to roll the die 100 times: Let \(Y\) be the number of times a yellow face is showing, \(R\) be the number of times a red face is showing, and \(O\) be the number of times an orange face is showing. Find the given probabilities, rounded to 4 decimal places:
\(P(O = 52)\)
\(P(R < 40)\)
\(P(Y \geq 10)\)
\(P(O > 55)\)
\(P(R = 35)\)
\(P(Y< 5)\)
\(P(45 < O < 55)\)
\(P(R \leq 30)\)
\(P(Y \geq20)\)
\(P(O < 40)\)
The following exercises are about series of games, where Team A faces Team B in a best-of series (like the World Series). Find the probability that Team A wins the series in each of the following scenarios:
Give the table of the PDF for flipping a fair coin 5 times and counting the heads. Do the calculations without using technology.
Give the table of the CDF for flipping a fair coin 5 times and counting the heads. Do the calculations without using technology.
The following exercises are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36, along with a “double zero”) and a color (0 and 00 are both green; the other 36 numbers are evenly divided between black and red). Players make bets on which number (or groups of numbers) they think the marble will land on. The figure shows the layout of the numbers and colors, as well as some of the bets that can be made.
If a player bets $1 on red and wins, the player gets $2 back (the original $1 bet plus $1 winnings). What is the probability that the player wins more than they lose if the player bets on red on 5 consecutive spins?
What is the probability that the player wins more than they lose if the player bets on red on 15 consecutive spins?
What is the probability that the player wins more than they lose if the player bets on red on 30 consecutive spins?
What is the probability that the player wins more than they lose if the player bets on red on 100 consecutive spins?
What is the probability that the player wins more than they lose if the player bets on red on 200 consecutive spins?
What is the probability that the player wins more than they lose if the player bets on red on 1,000 consecutive spins?
What is the probability that the player wins more than they lose if the player bets on red on 5,000 consecutive spins?
7.10.0: Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.
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