Calculate the probability for the following questions. a. A drawer contains 6 re

Question

Calculate the probability for the following questions. a. A drawer contains 6 red socks, 4 green socks, and 2 black socks. Two socks are chosen at random. What is the probability that they match? b. Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose P(V) = 0.15, P(W) = 0.05, and P(V W) = 0.17. (i) Find the probability that the computer contains both a virus and a worm. (ii) Find the probability that the computer contains neither a virus nor a worm. (iii) Find the probability that the computer contains a virus but not a worm.

Explanation / Answer

a)
P(match) = P(Red and Red) + P(Green and Green) + P (Black and Black)
P(Red and Red) = 6/12 * 5/11 = 5/22 = 15/66
P(Green and Green) = 4/12 * 3/11 = 2/22 = 6/66
P (Black and Black) = 2/12 * 1/11 = 1/66
P(match) = (15+6+1) / 66 = 22/66 = 1/3

b)
P(V) = 0.15
P(W) = 0.05
P(V U W) = 0.17

i)
P(V and W) = P(V) + P(W) - P(V U W)
P(V and W) = 0.15 + 0.05 - 0.17 = 0.03

ii)P(neither V nor W) = 1 - P(V U W) = 1 - 0.17 = 0.83

iii)P(V and not W) = P(V U W) - P(W) = 0.17 - 0.05 = 0.12

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