A coin is tossed successively three times. Find the Probability (P), Event…
2024
A coin is tossed successively three times. Find the Probability (P), Event (E), Sample space (S) of getting exactly one head or two heads, where n is number of occurrence.
(A) n(S) = 8 and n(E) = 4
(B) n(E) = 6 and n(S) = 8
(C) P(E) = 3/4
(D) P(E) = 1/2
Choose the correct answer from the options given below:
Answer: B. (B) and (C) — The sample space (S) for tossing a coin three times has 23=8 possible outcomes (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT), so n(S)=8. The event (E) requires…
- A.
(A), (B), (C) and (D)
- B.
(B) and (C)
- C.
(A) and (D)
- D.
(C) and (D)
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Correct answer: B
The sample space (S) for tossing a coin three times has 23=8 possible outcomes (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT), so n(S)=8. The event (E) requires getting "exactly one head" (HTT, THT, TTH) or "exactly two heads" (HHT, HTH, THH). There are 3 outcomes for one head and 3 outcomes for two heads, making the total favorable outcomes n(E)=3+3=6. Consequently, the probability P(E)=n(E)/n(S) =6/8=3/4. Therefore, only statements (B) and (C) are correct.
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