When a balanced coin is tossed four times, 16 equally likely outcomes are possible, as shown in the following table.
Let
A = event the first toss is heads,
B = event the second toss is tails, and
C = event the last two tosses are heads.
Apply the definition of independence for three events stated in Exercise 4.204 to show that A, B, and C are independent events.
In E 4.204
P(A & B) = P(A) · P(B),
P(A & C) = P(A) · P(C),
P(B & C) = P(B) · P(C), and
P(A & B & C) = P(A) · P(B) · P(C).
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