Likelihood Ratio tests

Question

I am trying to figure out how to calculate an LRT for a question, but my problem seems to start with the fact that I have no idea how this is possible:

$$\ln L1 = \ln(100/63) + 63 \ln(1/2) +(100-63)\ln(1-1/2) = -5.92.$$

Regardless of which calculator I send it to, I do not get this answer. What am I doing wrong, I am at a complete loss.

Answer 1

What is the probability that you get exactly $63$ heads in $100$ flips of a fair coin? [Then take the logarithm.] For some reason you thought it was $\frac{63}{100} (1/2)^{63} (1/2)^{100-63}$ or something, which is wrong.

$$\ln L_1 = \ln \left(\binom{100}{63} 2^{-100}\right) = - 100 \ln 2 + \sum_{k=64}^{100} \ln(k) - \sum_{k=1}^{37} ln(k) = -5.92$$