Question

Consider a biased coin with the probability of turning up head 0 < p < 1. We flip the coin 10 times and get a sequence of outcomes: {T, H, H, T, T, H, H, H, T, H}. We know that the probability (likelihood) of observing this sequence.

Answer 1

Probability of obtaining 6H and 4T = 0.2051

Explanation:

Since for a fair coin,

Probability of obtaining Head = 0.5

p = 0.5

q = 1-p = 0.5

Probability of obtaining 6H and 4T = 10C6 (p)^6(q)^4 = 210*0.5^6*0.5^4

P(6H, 4T) = 0.2051