In: Statistics and Probability
A husband and wife claim that they have a special bond that allows them to communicate by ESP. To test this claim, an researcher puts the husband and wife in separate rooms. The husband is randomly shown one of 5 colors: either blue, red, green, yellow or orange. He then is given 5 seconds to use his ESP to communicate the color to his wife. The wife then has to decide which of the 5 colors she was shown. This process is repeated 100 times. The wife correctly identifies the color 26 out of the 100 times. The null hypothesis is that she just guessed her husband's answers.
What is the EV (expected value) of the sum of the draws?
Show your work and explain your answer in words.