Question

In a carnival game, a player spins a wheel that stops with the pointer on one...

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 61 percent BLUE, 22 percent RED, and 17 percent GREEN. Note: Your answers should be rounded to three decimal places.

(a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is the probability that we will spin the wheel exactly three times?

(b) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on RED. What is the probability that we will spin the wheel at least three times?

(c) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on GREEN. What is the probability that we will spin the wheel 2 or fewer times?

Homework Answers

Answer #1

a)

Required probability = P(we will spin the wheel exactly three times) = P(the pointer stops for the first time at Blue on 3rd spin) = (1-0.61)(1-0.61)(0.61) = 0.093

b)

Required probability = P( we will spin the wheel at least three times) = 1 - P( we will spin the wheel less than three times)

= 1 - P( we will spin the wheel once) - P( we will spin the wheel twice)

= 1 - (0.22) - (1-0.22)(0.22) = 0.608

c)

Required probability = P( we will spin the wheel 2 or fewer times)

= P( we will spin the wheel once) + P( we will spin the wheel twice)

= 0.17 + (1-0.17)(0.17) = 0.311

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In a carnival game, a player spins a wheel that stops with the pointer on one...
In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 64 percent BLUE, 23 percent RED, and 13 percent GREEN. (a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is the probability that we will spin the wheel exactly three...
on a game show a contestants have a chance to spin a wheel. the wheel is...
on a game show a contestants have a chance to spin a wheel. the wheel is divided into slots, half of the slots say win and half say lose. there is a pointer above the top of the wheel, if the pointer points to a win slot when the wheel stops then the contestant wins cash prize. if the pointer points to a lose slot then the contestant wins nothing. The contestant spins the wheel 3 times. Let x be...
Roulette is a game of chance that involves spinning a wheel that is divided into 38...
Roulette is a game of chance that involves spinning a wheel that is divided into 38 equal segments, as shown in the accompanying picture. An image of a roulette wheel is shown. Text to the side of the image reads "©Anna Baburkina/Shutterstock.com." A metal ball is tossed into the wheel as it is spinning, and the ball eventually lands in one of the 38 segments. Each segment has an associated color. Two segments are green. Half of the other 36...
Suppose you are conducting an experiment consisting of rolling a twelve sided die, spinning a wheel...
Suppose you are conducting an experiment consisting of rolling a twelve sided die, spinning a wheel with equal sections in the colors of the rainbow (red, orange, yellow, green, blue, indigo, violet), and flipping a coin. What is the probability of getting a 5 or higher on the die roll, landing on a primary color on the wheel, and getting heads on the coin flip?
A carnival game involves a spinner that is designed so that in 20 percent of spins...
A carnival game involves a spinner that is designed so that in 20 percent of spins the player will win a prize. A random sample of 100 spins will be observed and the random variable X = number of times in the sample that the player won a price will be recorded. For the questions below, consider the process of finding the indicated probability by using the normal distribution as an approximation, including making the appropriate continuity correction. (Note that...
Suppose that, as part of a game at a charity carnival, players are invited to spin...
Suppose that, as part of a game at a charity carnival, players are invited to spin a wheel for a chance at winning either a small, medium, or large prize. The wheel is constructed so that the probability that a player wins a small prize, p, is 0.40. If a random sample of 40 players is selected, then ?̂  is the proportion of players in the sample who win a small prize. What is the mean of the sampling distribution of...
The likelihood of two fraudulent dice coming in pairs is six times the likelihood of a...
The likelihood of two fraudulent dice coming in pairs is six times the likelihood of a single coming. The opposite faces of these dice are painted in for the same color, in three color. Both dice are painted 1 to 6 red, 2 to 5 green and 3 to 4 blue colors. Two dice are being thrown together. The X-rassal variable is 0, if is the same color as the colors on the faces on top. The X-rassal variable is...
In a game show, a wheel of fortune is rotated 3 times with three sectors of...
In a game show, a wheel of fortune is rotated 3 times with three sectors of the same size in the colors blue, red and yellow. What is the probability of the following events? a.) The wheel does not stop in any of the 3 attempts in the red sector. ´= b.) The blue sector is hit exactly twice. = c.) The sector with the color yellow appears at least twice.= You can enter your results in the form of...
In the the casino game of roulette, players make bets based on a wheel with 38...
In the the casino game of roulette, players make bets based on a wheel with 38 numbered pockets (18 red pockets, 18 black pockets, and two green pockets, labeled 0 and 00). The wheel is then spun one direction and the ball is spun in the opposite direction. Eventually, the ball will land in one of the numbered pockets. The wheel is designed so that the ball has an equal chance of landing in any one of the pockets. Suppose...
Roulette USE SOFTWARE- In the casino game of roulette there is a wheel with 19 black...
Roulette USE SOFTWARE- In the casino game of roulette there is a wheel with 19 black slots, 19 red slots, and 2 green slots. In the game, a ball is rolled around a spinning wheel and it lands in one of the slots. It is assumed that each slot has the same probability of getting the ball. This results in the table of probabilities below. Fair Table Probabilities   black     red     green   Probability   19/40 19/40 2/40 You watch the game at...