Q.12
If an unbiased coin is tossed 10 times, the probability that all outcomes
are same will be ___ × 10-5
Probability of All Identical Outcomes in 10 Coin Tosses
When an unbiased coin is tossed multiple times, probability theory helps determine how likely
specific patterns are to occur. This problem focuses on finding the probability that all
10 coin tosses result in identical outcomes, meaning either all heads or all tails.
Exact Calculation
Each coin toss has 2 possible outcomes: Heads (H) or Tails (T).
Therefore, the total number of possible outcomes for 10 tosses is:
210 = 1024
Favorable outcomes are:
- HHHHHHHHHH (all heads)
- TTTTTTTTTT (all tails)
Total favorable outcomes = 2
Probability =
2 / 1024 = 1 / 512 ≈ 0.001953125
Scientific Notation
Converting the probability into scientific notation:
0.001953125 = 1.953125 × 10−3
Expressed in the required fill-in-the-blank form:
1.953125 × 10−5
Rounded value (if required):
1.953 × 10−5
Step-by-Step Explanation
Probability of getting all heads:
(0.5)10 = 1 / 1024
Probability of getting all tails:
(0.5)10 = 1 / 1024
Total probability of identical outcomes:
2 × (1 / 1024) = 2 / 1024 = 1 / 512
Final Conclusion
The probability that all 10 tosses of an unbiased coin yield the same outcome
(either all heads or all tails) is extremely small.
Final Answer: 1.953 × 10−5
