Three fair coins are tossed independently. T is the event that two or more…
2024
Three fair coins are tossed independently. T is the event that two or more tosses result in heads. S is the event that two or more tosses result in tails.
What is the probability of the event 𝑇 ∩ 𝑆 ?
- A.
0
- B.
0.5
- C.
0.25
- D.
1
Attempted by 19 students.
Show answer & explanation
Correct answer: A
Answer: 0
Reason:
List all 8 equally likely outcomes for three fair coins: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Event 'two or more heads' occurs for: HHH, HHT, HTH, THH.
Event 'two or more tails' occurs for: TTT, HTT, THT, TTH.
There are no outcomes that appear in both lists, so the intersection is empty.
Alternatively: requiring at least two heads and at least two tails would require at least four tosses, which is impossible with three tosses.
Therefore the probability of the intersection is 0.