Problem 1 (8 points) Three dice were rolled. Given that no two faces were the sa

Question

Problem 1 (8 points) Three dice were rolled. Given that no two faces were the same, what is the probability that there was a "1 What is the probability of throwing an 11 at least three times in five throws of a pair of fair dice? a) b) Problem 2 (8 points) a) If the unemployment rate in Canada is 5%, what is the probability that a random sample of 10,000 will contain between 450 and 550 unemployed? b) An oil well is to be drilled in a certain location where the soil is either rock (probability 0.53), clay (probability 0.21), or sand. If it is a rock, a geological test gives a positive result with 35% accuracy, if it is clay, this test gives a positive result with 45% accuracy, and if it is sand, the test gives a positive result with 75% accuracy. Given that the test is positive, what is the probability that the soil is rock?

Explanation / Answer

a) all faces are distinct

hence total number of sample space = 6*5*4 = 120

if there was not 1

hence number of sample space = 5*4*3 = 60

hence

required probability = 1 - 60/120 = 1/2 = 0.5

2)a)

p = 0.05

n = 10000

sd(p^)= sqrt(pq/n) = sqrt(0.05*0.95/10000) = 0.002179

P(450 < X< 550)

= P(0.045 < p < 0.055)

=

P ( 2.29<Z<2.29 )=0.978

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