Suppose we flip a fair coin three times. Define the following events: • A: the first flip is heads. • B: exactly one flip is heads. • C: the last flip is heads. • D: exactly two flips are heads. For each possible pair of these events, determine whether they are independe they are disjoint.
Suppose we flip a fair coin three times. Define the following events: • A: the first flip is heads. • B: exactly one flip is heads. • C: the last flip is heads. • D: exactly two flips are heads. For each possible pair of these events, determine whether they are independe they are disjoint.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:Suppose we flip a fair coin three times. Define the following events:
• A: the first flip is heads.
• B: exactly one flip is heads.
• C: the last flip is heads.
• D: exactly two flips are heads.
For each possible pair of these events, determine whether they are independent and whether
they are disjoint.
Expert Solution
Step 1
Suppose we flip a fair coin three times. We have the sample space as,
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let us define the following events:
A: the first flip is heads
B: exactly one flip is heads
C: the last flip is heads
D: exactly two flips are heads.
Thus, we have,
A = {HHH, HHT, HTH, HTT)
∴ P(A) = 4/8 = 0.5
B = {HTT, THT, TTH}
∴ P(B) = 3/8 = 0.375
C = {HHH, HTH, THH, TTH}
∴ P(C) = 4/8 = 0.5
D = {HHT, THH, HTH}
∴ P(D) = 3/8 = 0.375
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