suppose that 71% of the surface of the earth is covered in water, and a random number generator uses…

suppose that 71% of the surface of the earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the earth. if 7 such locations are generated, what is the probability that the first 5 locations are in water and the last 2 locations are on land?\n0.0010\n0.0152\n0.0910\n0.9090

suppose that 71% of the surface of the earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the earth. if 7 such locations are generated, what is the probability that the first 5 locations are in water and the last 2 locations are on land?\n0.0010\n0.0152\n0.0910\n0.9090

Answer

Answer:

0.0152

Explanation:

Step1: Determine probability of water and land

The probability of a location being in water $p = 0.71$, and the probability of a location being on land $q=1 - 0.71=0.29$.

Step2: Use multiplication rule for independent events

Since the selections are independent, the probability that the first 5 locations are in water and the last 2 are on land is $P=p^5\times q^2$.

Step3: Calculate the result

$P = 0.71^5\times0.29^2=(0.71^5)\times(0.29^2)\approx0.1804\times0.0841\approx0.0152$.