CAHSEE practice: Problems 13-14

Problem 13. These eight cards are placed face down and shuffled. So these are the eight cards. If Beatrice turns over only one card, what is the probability that she will get a card with a number less than four? So all of these cards right here are potential outcomes. She's going to flip them all over. And then she wants to know the probability that she gets a card less than four. So what are the cards that satisfy that? Well, there's three cards that are less than four. They didn't say less than or equal to four. So it could be that card, that card, or that card. Those are the cards that she can pick, out of the eight cards, that would satisfy this constraint. Or those would be the three outcomes, out of the eight possible outcomes, that would satisfy these conditions. So the probability is just three cards that satisfy your condition divided by the total number of outcomes. So the probability of her picking a card that is less than four-- there's three cards that are less than four out of eight cards. The probability is 3/8. And that is choice B. Always nice when our answer is actually there. OK. Problem-- what's the next problem? Problem 14. The Smithburg town library wanted to see what types of books were borrowed most often. All right, there we go. They drew a little pie diagram. According to the circle graph shown above-- OK, let's see which of these statements are true. The first statement says, "more Children's books were borrowed than Romance and Science Fiction combined." Let's see if that's true. Children's is 26%, and then Romance and Science Fiction combined. Romance is 13, and Science Fiction is 18. So what's 13 plus 18? 3 plus 8 is 11. And then we have 1 plus 1 plus 1. And so then we get 31. So if you take Romance and Science Fiction combined, that's 31% of the books, while the Children's books were only 26%. So that is definitely not correct. More than half of the books borrowed were Children's, Mysteries, and Art combined. So more than half would mean it has to be more than 50%. So they think Children's, Mysteries, and Art combined. So let's see what that gets. Children's-- I'll do it in a different color. Children's, Mysteries, and Art. So Children's and Mysteries, if you add those together, 26 plus 20, that gives you 46%. And then you add another 4% to that. We're combining with Art. That gets us to 50%. So exactly half the books borrowed were Children's, Mysteries, and Art. But they're saying more than half. This is exactly half. So this doesn't seem right either. If they said half or more, then we would have picked this choice. But they said definitely more than 50%, so that can't be it. Although it's kind of a tricky one, because it's exactly 50%. C, more Mysteries were borrowed than Art and Science Fiction combined. Mysteries was 20%, and then Art and Science Fiction combined is 4 plus 18. If you combine these two, you get 4 plus 18 is 22%. So the Mysteries are definitely not more than the Art and Science Fiction combined. So that's not the correct answer. And then finally, more than half of the books-- this is probably going to be our answer, if we haven't made any silly mistakes. This says more than half of the books borrowed were Romance, Mysteries, and Science Fiction combined. Let's see that. Romance, Mysteries, and Science Fiction. We already know Romance plus Science Fiction, that was 13 plus 18, which we already figured out was 31%. These two could combine at 31%, and then you add that 31% to the Mysteries. So it becomes 51%. So that's right. This is 51% of the books borrowed. So that's definitely more than half of the books, so the correct choice here is D.