Question

Barbara claims that her horse can do simple addition problems. She showed her horse eight different cards with simple addition problems, and the horse was able to tap his foot to indicate whether the answer was correct or incorrect. The horse correctly identified all eight cards. Eric didn't believe Barbara's horse could do addition, so he set up a trial to test whether the horse was just guessing. He flipped eight coins to see how many would land tails up. He did this 53 times, and the results are shown in the dot plot below: A dot plot with values of 1, 2 3, 4, 5, 6, 7, 8 corresponding to frequencies of 3, 5, 8, 11, 8, 7, 5, and 1 respectively. Based on these results, can Barbara's horse add?

Answer 1

Yes, the chances of getting 8 correct by guessing are very low

Answer 2

Barbara's horse can add

Explanation:

To test if the horse could add, Eric he tried to calculate experimentally the probability that the horse had guessed the 8 answers.

If we call "trial" the action of throwing 8 coins and count the number of tails obtained, then eric made 53 trials.

During each trial, 8 events could have occurred:

Get 1, 2, 3, 4, 5, 6, 7 or 8 tails.

The plot of points obtained by Eric shows the frequency in which each of these 8 events occurred during the 53 trials.

The fact that the point diagram shows only one point on event 8, means that it occurred only once during the 53 trials, and compared to the other 7 events, this was the one with a lower frequency (the one that obtained the the highest frequency was the 4-tailed one, with 11 points).

This means that it is very unlikely to get 8 queues when casting 8 coins.

Therefore it also means that it is unlikely that Barbara's horse has guessed the 8 answers.

So, curiously, Barbara's horse maybe knows how to add