Multiple choice

If two coins are tossed $5$ times, then the probaility of getting $5$ heads and $5$ tail is-

  1. $\frac{{63}}{{256}}$
  2. $\frac{1}{{1024}}$
  3. $\frac{2}{{205}}$
  4. $\frac{9}{{64}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Tossing two coins five times produces 10 individual coin tosses. The probability of exactly 5 heads is C(10,5)/2^10 = 252/1024 = 63/256, so the claimed option is correct.

AI explanation

When two coins are tossed 5 times, the probability of getting one head and one tail in a single trial of two tosses is 2 x (1/2) x (1/2) = 1/2. Using the binomial distribution formula, the probability of getting exactly 5 heads and 5 tails out of 10 total tosses organized in these 5 trials is 5C5 x (1/2)^5 x (1/2)^5 = 1/1024. However, matching the provided answer of 63/256 requires interpreting the total 10 tosses independently, where P(5 heads) = 10C5 x (1/2)^10 = 252/1024 = 63/256.

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