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Chapter 4: Problem 5
In a group of adults, some own iPads, and others do not. If two adults are randomly selected from this group, how many total outcomes are possible? Draw a tree diagram for this experiment.
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A sample of 400 large companies showed that 130 of them offer free health fitness centers to their employees on the company premises. If one company is selected at random from this sample, what is the probability that this company offers a free health fitness center to its employees on the company premises? What is the probability that this company does not offer a free health fitness center to its employees on the company premises? Do these two probabilities add to \(1.0 ?\) If yes, why?
A statistical experiment has 11 equally likely outcomes that are denoted by \(a, b, c, d, e, f, g, h, i, j\), and \(k .\) Consider three events: \(A=\\{b, d, e, j\\}, B=\\{a, c, f, j\\}\), and \(C=\\{c, g, k\\}\) a. Are events \(A\) and \(B\) independent events? What about events \(A\) and \(C ?\) b. Are events \(A\) and \(B\) mutually exclusive events? What about \(A\) and \(C\) ? What about \(B\) and \(C\) ? c. What are the complements of events \(A, B\), and \(C\), respectively, and what are their probabilities?
A thief has stolen Roger's automatic teller machine (ATM) card. The card has a four-digit personal identification number (PIN). The thief knows that the first two digits are 3 and 5 , but he does not know the last two digits. Thus, the PIN could be any number from 3500 to \(3599 .\) To protect the customer, the automatic teller machine will not allow more than three unsuccessful attempts to enter the PIN. After the third wrong PIN, the machine keeps the card and allows no further attempts. a. What is the probability that the thief will find the correct PIN within three tries? (Assume that the thief will not try the same wrong PIN twice.) b. If the thief knew that the first two digits were 3 and 5 and that the third digit was either 1 or 7 , what is the probability of the thief guessing the correct PIN in three attempts?
What is meant by the joint probability of two or more events? Give one example.
Consider the following addition rule to find the probability of the union of two events \(A\) and \(B\) : $$ P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B) $$ When and why is the term \(P(A\) and \(B\) ) subtracted from the sum of \(P(A)\) and \(P(B) ?\) Give one example where you might use this formula.
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