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# CAHSEE practice: Problems 13-14

Video transcript

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.