Question: 2015 Winter Final - 16
Consider a bitstring of length 77, in which each bit is 0 with probability 1/3 (and, thus, 1 with
probability 2/3), independently of the other bits. What is the probability that there are exactly
15 0s in this bitstring?
(a)
${77 \choose 15}(1/3)^{15}(2/3)^{62}$
(b)
${77 \choose 15}((1/3)^{15} + (2/3)^{62})$
(c)
${77 \choose 15}(1/3)^{62}(2/3)^{15}$
(d)
${77 \choose 15}((1/3)^{62} + (2/3)^{15})$