Question

an experiment consists of tossing 7 fair (not weighted coins) except one of the 7 has heads on both sides. Compute the probability of obtaining exactly 5 heads.

Answer 1

One of the 7 coins has heads on both sides. So, tossing of that coin will always result heads.

So, the probability of obtaining exactly 5 heads = probability of obtaining exactly 4 heads from remaining 6 fair coins with heads and tails on their sides.

Probability of getting heads, p = 1/2

So, the number of heads X in tossing of 6 coins follow Binomial distribution with parameters n = 6 and p = 1/2 = 0.5

P(X = 4) = ⁶C₄ * 0.5⁴ * (1 - 0.5)²

= 15 * 0.5⁶

= 0.234375