What is probability? A probability is a numerical measure greater than or equal to and less than or equal to that describes the likelihood that an event will occur. Probabilities closer to indicate that the event is more likely to occur. Probabilities closer to indicate that the event is less likely to occur. What do we mean by relative frequency as a probability estimate for events? A probability assignment based on relative frequency uses the formula, probability of event = relative frequency = , where f is the frequency of the event occurrence in a sample of n observations.

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The Hill of Tara is located in south-central Meath, not far from Dublin, Ireland. Tara is of great cultural and archaeological importance, since it is by legend the seat of the
ancient high kings of Ireland. For more information, see Tara: An Archaeological Survey, by Conor Newman, Royal Irish Academy, Dublin.
Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic
susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a
randomly chosen site on the Hill of Tara. A random sample of 120 sites gave the readings shown in the table below.
Magnetic Susceptibility Readings,
centimeter-gram-second x 10-6 (cmg x 10-6)
Magnetic
Susceptibility
Number of
Readings
Estimated
Comment
Probability
"cool"
Osx< 10
30
30/120 = 0.25
"neutral"
10 <x < 20
54
54/120 = 0.45
"warm"
20 <x < 30
18
18/120 = 0.15
"very interesting"
"hot spot"
30 sx < 40
40 sx
12/120 = 0.10
6/120 = 0.05
12
6
What is probability?
A probability is a numerical measure greater than or equal to
and less than or equal to
that describes the likelihood that an event will occur.
Probabilities closer to
indicate that the event is more likely to occur. Probabilities closer to
indicate that the event is less likely to occur.
What do we mean by relative frequency as a probability estimate for events?
A probability assignment based on relative frequency uses the formula, probability of event = relative frequency =
, where f is the frequency of the
event occurrence in a sample of n observations.
Transcribed Image Text:The Hill of Tara is located in south-central Meath, not far from Dublin, Ireland. Tara is of great cultural and archaeological importance, since it is by legend the seat of the ancient high kings of Ireland. For more information, see Tara: An Archaeological Survey, by Conor Newman, Royal Irish Academy, Dublin. Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site on the Hill of Tara. A random sample of 120 sites gave the readings shown in the table below. Magnetic Susceptibility Readings, centimeter-gram-second x 10-6 (cmg x 10-6) Magnetic Susceptibility Number of Readings Estimated Comment Probability "cool" Osx< 10 30 30/120 = 0.25 "neutral" 10 <x < 20 54 54/120 = 0.45 "warm" 20 <x < 30 18 18/120 = 0.15 "very interesting" "hot spot" 30 sx < 40 40 sx 12/120 = 0.10 6/120 = 0.05 12 6 What is probability? A probability is a numerical measure greater than or equal to and less than or equal to that describes the likelihood that an event will occur. Probabilities closer to indicate that the event is more likely to occur. Probabilities closer to indicate that the event is less likely to occur. What do we mean by relative frequency as a probability estimate for events? A probability assignment based on relative frequency uses the formula, probability of event = relative frequency = , where f is the frequency of the event occurrence in a sample of n observations.
What is the law of large numbers? How would the law of large numbers apply in this context?
O The law of large numbers states that as the number of trials decreases, the relative frequency approaches the theoretical probability. If we took more and more
readings, the relative frequencies would become more accurate estimates of the true probabilities.
O The law of large numbers states that as the number of trials increases, the relative frequency approaches the theoretical probability. If we took more and more readings,
the relative frequencies would become less accurate estimates of the true probabilities.
O The law of large numbers states that for any number of trials, the relative frequency is the same as the theoretical probability. If we took more and more readings, the
relative frequencies would always be perfect estimates of the true probabilities.
O The law of large numbers states that as the number of trials decreases, the relative frequency approaches the theoretical probability. If we took more and more
readings, the relative frequencies would become less accurate estimates of the true probabilities.
O The law of large numbers states that as the number of trials increases, the relative frequency approaches the theoretical probability. If we took more and more readings,
the relative frequencies would become more accurate estimates of the true probabilities.
Transcribed Image Text:What is the law of large numbers? How would the law of large numbers apply in this context? O The law of large numbers states that as the number of trials decreases, the relative frequency approaches the theoretical probability. If we took more and more readings, the relative frequencies would become more accurate estimates of the true probabilities. O The law of large numbers states that as the number of trials increases, the relative frequency approaches the theoretical probability. If we took more and more readings, the relative frequencies would become less accurate estimates of the true probabilities. O The law of large numbers states that for any number of trials, the relative frequency is the same as the theoretical probability. If we took more and more readings, the relative frequencies would always be perfect estimates of the true probabilities. O The law of large numbers states that as the number of trials decreases, the relative frequency approaches the theoretical probability. If we took more and more readings, the relative frequencies would become less accurate estimates of the true probabilities. O The law of large numbers states that as the number of trials increases, the relative frequency approaches the theoretical probability. If we took more and more readings, the relative frequencies would become more accurate estimates of the true probabilities.
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