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Chapter 5: Problem 4

What does it mean to say that the probability that a coin toss will land head side up is \(0.5 ?\)

Short Answer

Expert verified
The probability \(0.5\) for a coin toss landing head side up means that there is an equal chance (50%) of the coin landing heads up or tails up. In larger number of tosses, heads would be expected to appear about half the time.

Step by step solution

01

Understand the concept of probability

Probability is a measurement of the likelihood that an event will happen. It is a value between 0 and 1, inclusive. A probability of 1 means the event is certain to happen, a probability of 0 means the event will not happen, and a probability of 0.5 suggests the event is equally likely to happen or not happen.
02

Apply the concept to the given situation

In the context of a coin toss, there are two possible outcomes: heads or tails. If the coin is fair (i.e., not biased), then each side has an equal chance of appearing. Therefore, the probability is \(0.5\) or 50% for each.
03

Interpret the probability

To say that the probability that a coin toss will land head side up is \(0.5\) means that, for a large number of coin flips, we would expect heads to appear approximately half of the time. In other words, if the coin is flipped 100 times, we would expect to see about 50 heads. This doesn't mean every 100 flips will produce exactly 50 heads, but rather, this is the expected average over repeated trials.

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Most popular questions from this chapter

A Gallup survey found that \(46 \%\) of women and \(37 \%\) of men experience pain on a daily basis (San Luis Obispo Tribune, April 6,2000 ). Suppose that this information is representative of U.S. adults. If a U.S. adult is selected at random, are the events selected adult is male and selected adult experiences pain on a daily basis independent or dependent? Explain.

A student placement center has requests from five students for employment interviews. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students. These two will be randomly selected from among the five. a. What is the sample space for the chance experiment of selecting two students at random? (Hint: You can think of the students as being labeled \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D},\) and \(\mathrm{E}\). One possible selection of two students is \(\mathrm{A}\) and \(\mathrm{B}\). There are nine other possible selections to consider.) b. Are the outcomes in the sample space equally likely? c. What is the probability that both selected students are statistics majors? d. What is the probability that both students are math majors? e. What is the probability that at least one of the students selected is a statistics major? f. What is the probability that the selected students have different majors?

The article "Checks Halt over 200,000 Gun Sales" (San Luis Obispo Tribune, June 5,2000 ) reported that required background checks blocked 204,000 gun sales in \(1999 .\) The article also indicated that state and local police reject a higher percentage of would-be gun buyers than does the FBI, stating, "The FBI performed 4.5 million of the 8.6 million checks, compared with 4.1 million by state and local agencies. The rejection rate among state and local agencies was \(3 \%,\) compared with \(1.8 \%\) for the FBI." a. Use the given information to estimate \(P(F), P(S)\), \(P(R \mid F),\) and \(P(R \mid S),\) where \(F=\) event that a randomly selected gun purchase background check is performed by the \(\mathrm{FBI}, S=\) event that a randomly selected gun purchase background check is performed by a state or local agency, and \(R=\) event that a randomly selected gun purchase background check results in a blocked sale. b. Use the probabilities from Part (a) to create a "hypothetical \(1000 "\) table. Use the table to calculate \(P(S \mid R),\) and write a sentence interpreting this value in the context of this problem.

A large retail store sells MP3 players. A customer who purchases an MP3 player can pay either by cash or credit card. An extended warranty is also available for purchase. Suppose that the events \(M=\) event that the customer paid by cash \(E=\) event that the customer purchased an extended warranty are independent with \(P(M)=0.47\) and \(P(E)=0.16\). a. Construct a "hypothetical 1000 " table with columns corresponding to cash or credit card and rows corresponding to whether or not an extended warranty is purchased. (Hint: See Example 5.9) b. Use the table to find \(P(M \cup E)\). Give a long-run relative frequency interpretation of this probability.

An online store offers two methods of shipping-regular ground service and an expedited 2 -day shipping. Customers may also choose whether or not to have a purchase gift wrapped. Suppose that the events \(E=\) event that the customer chooses expedited shipping \(G=\) event that the customer chooses gift wrap are independent with \(P(E)=0.26\) and \(P(G)=0.12\). a. Construct a "hypothetical 1000 " table with columns corresponding to whether or not expedited shipping is chosen and rows corresponding to whether or not gift wrap is selected. b. Use the table to calculate \(P(E \cup G)\). Give a long-run relative frequency interpretation of this probability.
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