When two balanced dice are rolled, 36 equally likely outcomes are possible, as illustrated in Fig. 4.1

Question:

When two balanced dice are rolled, 36 equally likely outcomes are possible, as illustrated in Fig. 4.1 on page 159. Let
In Fig 4.1

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A = event the red die comes up even,
B = event the black die comes up even,
C = event the sum of the dice is even,
D = event the red die comes up 1, 2, or 3,
E = event the red die comes up 3, 4, or 5, and
F = event the sum of the dice is 5.
Apply the definition of independence for three events stated in Exercise 4.204 to solve each problem.
a. Are A, B, and C independent events?
b. Show that P(D & E & F) = P(D) · P(E) · P(F) but that D, E, and F are not independent events.