Question

Example 3.9 Let event G = taking a math class. Let event H = taking a science class. Then, G AND H = taking a math class and a science class. Suppose P(G) = 0.6, P(HT) = 0.5, and P(G AND H) = 0.3. Are G and Hindependent? This OpenStax book is available for free at http://cnx.org/content/col11562/1.18 Chapter 3 Probability Topics If G and H are independent, then you must show ONE of the following: • P(G|H) = P(G) • P(HG) = P(H) • P(G AND H) = P(G)P(H)

Answer 1

Go taking a math clan. Gro w ing Ha taking a suence clan... 4 kHz taking a math clan and a e Science clan. P(4) = 0.6, (a and H) = 0.3 P(HJ = 0.5 G and it . So, P(a and H) are independent of (a) e (6nH) = 0.3 P(G) xP (H.) = 0.6 80.5 iff P(40H) 2 P (C) xP (H) - 0.3

So, & G and it P (4 and H) = P (4) * P(H) So, 4 and I are independent are independent, P(G)H) - conditional probability of G and it. a P(ant) i P (H) м 2 Насе P(G) XP(H) independent PCH) - P(4) (Proced)

P(+14) = P(+14) PCH P(4x P(Hg are independent i= PCA o PCG) 10H

P(+14) = P(+14) PCH P(4x P(Hg are independent i= PCA o PCG) 10H