3.(16 points) A Spot Ulility Vehicle (SUV) manufacturing company Drof Inc. manuf

Question

3.(16 points) A Spot Ulility Vehicle (SUV) manufacturing company Drof Inc. manufactures 4 types of SUV's named: All terrain, Bumpy-roads, Cargo-king, and, Dude-city. Drof Inc's SUVs come with tires that are sometimes made by company. Ent Serif. Drof announced that 20% of their SUVs that have been sold are All-terrains, 30% are Bumpy-roads, 40% are Cargo-king, and, 10% are Dude-city. Also announced is the fact that 50%of All-terrains use Enot Serif tires, 60% of Bumpy-roads, use Enot Serif tires, 70% of Cargo-kings use Enot Serif tires, whereas none of the Dude-city SUVs have Enot Serif tires. Given below are events: A Drof SUV is All-terra,T z A B-, Drof SUV is Bumpy-roads, ? (B) , . 3 P(B1E> : C = Drof. SUV is Cargo-king, (c): , 7/r D-Drof SUV is Dude-city, and Plt): . E Drof SUV uses Enot Serif tires. 1 (V18) 2-3-4 1.C

Explanation / Answer

P(E | A) = 0.5

P(E | B) = 0.6

P(E | C) = 0.7

P(E | D) = 0

P(E) = P(E | A) * P(A) + P(E |B) * P(B) + P(E | C) * P(C) + P(E | D) * P(D)

= 0.5 * 0.2 + 0.6 * 0.3 + 0.7 * 0.4 + 0 * 0.1

= 0.56

P(A | E) = P(E | A) * P(A) / P(E)

= 0.5 * 0.2 / 0.56

= 0.18

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