A recent study of young executives showed that 30 percent run, 20 percent bike and 12 percent do both. What is the percent of young executives who run or bike?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Answer each question below. Be sure to show all of your work.
1. A recent study of young executives showed that 30 percent run, 20 percent bike and 12 percent do both. What is the percent of young executives who run or bike?
2. A survey of publishing jobs indicates that 92 percent are completed on time. Assume that three jobs are selected for study.
a. What is the probability they are all completed on time?
b. What is the probability that at least one was not completed on time?
3. Today’s local newspaper lists 20 stocks “of local interest.” Of these stocks, ten increased, five decreased and five remained unchanged yesterday. If we decide to buy two of the stocks, what is the likelihood that both increased yesterday?
4. Six employees of a marketing firm had effectiveness ratings as follows: 0.72, 0.46, 0.59, 0.64, 0.81 and 0.76. Find the probability of selecting an employee with the indicated effectiveness rating.
a. Greater than 0.75.
b. Less than 0.75 but greater than 0.5.
c. Greater than the mean.
d. Not less than 0.9.
5. A freight train is going to carry four tankers, six coal cars, and ten lumber cars. How many different arrangements of cars are possible?
Women
Men
Total
Under 30
30
8
38
30 to 50
25
14
39
50 & over
18
5
23
Totals
73
27
100
17. A market analyst is hired to provide information on the type of customers who shop at a particular store. A random survey is taken of 100 shoppers at this store. Of these 100, 73 are women. The shoppers are grouped in three age categories, under 30, 30 up to 50 and 50 and over. The data is summarized in the table.
Let W be the event that a randomly selected shopper is a woman.
Let A be the event that a randomly selected shopper is under 30.
a. Find the probability of (W.
b. Find the probability of A.
c. Find the probability of A and W.
d. Find the probability of A or (W.
e. Find the probability of A given W.
18. Perry’s Garden Center sells three brands of riding mowers—Ranger, Turfmaster, and Colt. Fifty percent of the riding mowers they sell are Rangers, thirty five percent Turfmasters, and fifteen percent Colts. Each brand of mower comes with a one-year parts and labor warranty. Based on their records, Perry knows that the chance of a warranty claim is five percent for the Ranger, 15% for the Turfmaster, and 25% for the Colt. If Perry’s service manager tells him that a riding mower has just been brought in for a repair covered by the warranty,.
a.Wahat is the chance that the riding mower is a Colt?
b.What is the chance that the riding mower is a Turfmaster?
c. What is the chance that the riding mower is a Ranger?
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