Listed below is the population by state (approximated to the nearest million) fo

Question

Listed below is the population by state (approximated to the nearest million) for the 15 states with the largest population. Also included is whether the state's border touches the Gulf of Mexico, the Atlantic Ocean, or the Pacific Ocean (coastline). Note that five of the 15 states do not have coastlines. Suppose three states are selected at random. What is the probability that: Rank State Population Coastline 1 California 37 Yes a) None of the states has any coastlines. 2 Texas 24 Yes 3 New York 19 Yes b) Exactly one of the selected states has a coastline? 4 Florida 18 Yes 5 Illinois 13 No c) At least one selected state has a coastline? 6 Pennsylvania 12 No 7 Ohio 11 No 8 Michigan 10 No 9 Georgia 10 Yes 10 North Carolina 9 Yes 11 New Jersey 9 Yes 12 Virginia 8 Yes 13 Washington 6 Yes 14 Massachusetts 6 Yes 15 Indiana 6 No

Explanation / Answer

Their are 15 states out of which 10 states having coastlines and 5 states may not have coastlines.

n = 15

x = states having coastlines

p = probability that states having coastlines = x /n = 10 /15 = 0.6667

q = probability that no states having coastlines = 5 / 15 = 0.3333

a)

P( None of the states has any coastline) = 5 / 15 = 0.3333

b)

P(exactly one of the selected state has a coastline) = (1 /10) * (10/15) = 0.0667

c)

P(At least one selected state has a coastline) = 10 / 15 = 0.6667

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