Chapter 4: Q.17 (page 283)
Find the probability that Javier volunteers for at least one event each month.
Short Answer
The probability that Javier volunteers for at least one event each month.
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Chapter 4: Q.17 (page 283)
Find the probability that Javier volunteers for at least one event each month.
The probability that Javier volunteers for at least one event each month.
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A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be . We are interested in the number of dealerships she must call.
a. In words, define the random variable .
b. List the values that X may take on.
c. Give the distribution of . ~ _____(_____,_____)
d. On average, how many dealerships would we expect her to have to call until she finds one that has the car?
e. Find the probability that she must call at most four dealerships.
f. Find the probability that she must call three or four dealerships
An electronics store expects to have ten returns per day on average. The manager wants to know the probability of the store getting fewer than eight returns on any given day. State the probability question mathematically.
There are two similar games played for Chinese New Year and Vietnamese New Year. In the Chinese version, fair dice with numbers 1, 2, 3, 4, 5, and 6 are used, along with a board with those numbers. In the Vietnamese version, fair dice with pictures of a gourd, fish, rooster, crab, crayfish, and deer are used. The board has those six objects on it, also. We will play with bets being \(1. The player places a bet on a number or object. The 鈥渉ouse鈥 rolls three dice. If none of the dice show the number or object that was bet, the house keeps the \)1 bet. If one of the dice shows the number or object bet (and the other two do not show it), the player gets back his or her \(1 bet, plus \)1 profit. If two of the dice show the number or object bet (and the third die does not show it), the player gets back his or her \(1 bet, plus \)2 profit. If all three dice show the number or object bet, the player gets back his or her \(1 bet, plus \)3 profit. Let X = number of matches and Y = profit per game.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. List the values that Y may take on. Then, construct one PDF table that includes both X and Y and their probabilities.
e. Calculate the average expected matches over the long run of playing this game for the player.
f. Calculate the average expected earnings over the long run of playing this game for the player
g. Determine who has the advantage, the player or the house.
At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the number of fencers who do not use the foil as their main weapon.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. How many are expected to not to use the foil as their main weapon?
e. Find the probability that six do not use the foil as their main weapon.
f. Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.
On average, how long would you expect a new hire to stay with the company?
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