Q.17 If a coin is tossed three times, what is the probability that NO two successive tosses show
the same face?
(A) 0.25 (B) 0.33 (C) 0.20 (D) 0.125
Sample Space
A fair coin tossed three times yields 2³ = 8 equally likely outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Each outcome has probability 1/8.
Favorable Outcomes
“No two successive tosses show the same face” means outcomes where consecutive results differ: first ≠ second, and second ≠ third. The valid sequences are HTH and THT.
- HTH: H≠T, T≠H
- THT: T≠H, H≠T
No other outcomes satisfy both conditions (e.g., HHT has first two same; HTT has last two same).
Probability Calculation
Number of favorable outcomes = 2. Total outcomes = 8. Thus, probability = 2/8 = 0.25 or 1/4.
Option Analysis
| Option | Value | Correct? | Reason |
|---|---|---|---|
| (A) | 0.25 | Yes | Matches 2/8.[web:16] |
| (B) | 0.33 | No | Equals 1/3; perhaps from miscounting 2-3 outcomes. |
| (C) | 0.20 | No | Equals 1/5; confuses with no consecutive heads (5/8=0.625). |
| (D) | 0.125 | No | Equals 1/8; probability of single outcome like HHH. |
Recursive Insight
For n tosses, let aₙ be number of valid sequences. Then a₁=2, a₂=2 (HT, TH), and aₙ=aₙ₋₁ (extend by opposite of last). For n=3, a₃=2. Probability = aₙ/2ⁿ = 2/8 = 0.25.
Why This Matters for CSIR NET
When exploring the coin tossed three times no two successive same face probability, this classic probability puzzle challenges students preparing for exams like CSIR NET. The keyphrase highlights a scenario where each pair of consecutive tosses must differ—essential for mastering sample spaces and favorable outcomes in competitive math.
In three coin tosses, total outcomes number 8, but only alternating patterns like HTH and THT qualify. This yields 2/8=0.25, option (A) in typical MCQs. Common traps include confusing it with “no consecutive heads” (5/8) or exact heads count.
