3. Linda took a multiple choice test. She did pretty well, but there were 5 questions where she had to guess. Each question had 4 choices for answers. Make up a probability distribution for the number of correct guesses. What is the probability that she got at least 2 right?

We use the formula

P(x) = C(n, x)pxqn-x

to compute the probabilities of all of the possible numbers of successes. The possible numbers of successes will be all of the whole numbers from 0 to 5, the number of trials.

For the probability that she got at least 2 right add up the probabilities of 2, 3, 4, and 5

270/1024 + 90/1024 + 15/1024 + 1/1024

= 376/1024

= 47/128

In this case it would be easier to compute the probability of the complementary event: none or one right.

243/1024 + 405/1024

= 648/1024

= 81/128

Our answer is the complementary probability which is computed by subtracting from 1, and it will check.