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 Dec 10, 2018
edited by shann0n  Dec 10, 2018
edited by shann0n  Dec 14, 2018

\(\text{If there are 8 T's there are 8 C's, so we are left with 14 slots}\\ \text{This means that A=G=7}\\ P[\text{8 T's}] = \dbinom{30}{8}\dbinom{22}{8}\dbinom{14}{7}(0.29)^7(0.23)^8(0.27)^7(0.21)^8\)


Now the problem might actually mean there are at least 8 T's.  In which case we'd modify above to be


\(\large \sum \limits_{t=8}^{15}~\dbinom{30}{t}\dbinom{30-t}{t}\dbinom{30-2t}{15-t}(0.29)^{15-t}(0.23)^t(0.27)^{15-t}(0.21)^t\)

 Dec 10, 2018

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