Brian claims that his dog can do single-digit multiplication. he shows the dog 10 cards with simple multiplication problems that are either correct or incorrect. the dog correctly identifies the correctness of the card 7 times out of 10. if the dog were simply guessing, how many would the dog be expected to get correct?

Step-by-step explanation:

X the number of correct answers the dog chooses by guessing

Then each guess is independent of the other.  Also there are only two outcomes either correct or not correct.

Since dog does not know the answer and there is simple guessing the dog selecting the correct answer = dog correcting noncorrect answer = 1/2

X is binomial (n =10 and p = 1/2)

Expected values of correct answers

=E(X)

=Mean of a binomial variable

=np

Here n =10 and p =1/2

Hence expected value of correct answers = 5

the answer is 15% decrease