Beach erosional hot spots. Beaches that exhibit high erosion rates relative to the surrounding beach are defined as erosional hot spots. The U.S. Army Corps of Engineers is conducting a study of beach hot spots. Through an online questionnaire, data are collected on six beach hot spots.

The data are listed in the next table.

a. Suppose you record the nearshore bar condition of each beach hot spot. Give the sample space for this experiment.

b. Find the probabilities of the sample points in the sample space you defined in part a.

c. What is the probability that a beach hot spot has either a planar or single, shore-parallel nearshore bar condition?

d. Now suppose you record the beach condition of each beach hot spot. Give the sample space for this experiment.

e. Find the probabilities of the sample points in the sample space you defined in part d.

f. What is the probability that the condition of the beach at a particular beach hot spot is not flat?

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Beach Hot Spot Beach Condition Nearshore Bar Condition Long-Term Erosion Rate (miles/year) Miami Beach, FL No dunes/flat Single, shore parallel 4 Coney No dunes/flat Other 13 Island, NY Surfside, CA Bluff/scarp Single, shore 35 parallel Monmouth Single dune Planar Not estimated Beach, NJ Ocean City, NJ Single dune Other Not estimated Spring Lake, NJ Not observed Planar 14