Setup for Problems $3-4.$ A distant alien language is written using an alphabet that has just three letters: $o+,,$ and

$ox.$ In plaintext of this language, $20\%$ of letters are $o+,$ another $20\%$ are $,$ and the remaining $60\%$ are $ox.$ Shohreh is a

human codebreaker who specializes in decrypting ciphertexts of this alien language. In a $1000-$letter ciphertext that

she has just intercepted, Shohreh finds that the three letters occur with the following counts:

Shohreh wonders if this ciphertext might be encrypted using a transposition cipher, so she would like to use a G$-$test

to determine if the observed counts are compatible with the hypothesis that the ciphertext letter frequencies follow

the letter frequencies of plaintext in this alien language.

Problem $3.$ Assuming the letter frequencies in Shohreh's ciphertext follow the letter frequencies of plaintext, how

many of the letters in the ciphertext are expected to be $o+?$