Question

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is

(A) 63/64

(B) 255/256

(C) 127/128

(D) 1/2

Answer 1

Answer is (C) 127/128

It is given that an unbiased coin is tossed eight times; thus, n = 8.

The probability of obtaining head is

p = 1/2

The probability of obtaining tail is q = 1/2

If x is the number of heads, then the probability that at least one head and at least one tail is obtained is expressed as 

1 – (Probability of all head + Probability of all tail) = 1 – [p(x = 8) + p(x = 0)]

Using identity p(x = r) = ⁿC_rp^rq^{n - r}, we can write as 1 – (Probability of all head + Probability of all tail)