name unit 4 applications of probability datei lesson 2 conditional probability practice 423 the

Name unit 4 applications of probability datei lesson 2...

Name: UNIT 4 APPLICATIONS OF PROBABILITY Date: Lesson 2: Conditional Probability Practice 4.2.3: The Multiplication Rule Use the following information to answer questions 1-4. Round each answer to the nearest thousandth. Harper keeps her textbooks in her locker: She has a biology book and 2 English books. Harper grabs textbooks at random. What is the probability that both books are history books? What is the probability that both books are English books? What is the probability that one book is a math book, and the other is a biology book? Is it more likely that Harper will pick 2 French books or 2 English books? Use the following information for questions 5-8. Round each answer to the nearest thousandth. Michael chooses a pair of socks and a pair of sneakers randomly each morning. The table below lists the colors and number of pairs of socks and sneakers he owns: Number of pairs by color: White: 3 Gray: 5 Black: 2 Blue: 4 Orange: 1 What is the probability that Michael selects both white socks and white sneakers? What is the probability that his socks are black and his sneakers are white? What is the probability that his socks are gray and his sneakers are black? What is the probability that he chooses both black socks and black sneakers? Is it more likely that he chooses both white socks and white sneakers?

Transcript

00:01 So there are eight different questions here, and the first four deal with the books that is in harper's locker.

00:07 So in her locker, we've got one math book, we've got two french books, we've got two history books, we've got one biology book, and we've got three english books, for a total of nine books.

00:36 So for question one, you're trying to determine the probability that when she reaches into the locker, that both books will be history books.

00:49 So you need to think of this as being dependent probability, because once one book is taken out, when you go in for the next book, there's fewer books in the locker.

01:01 So we want the probability of two history books.

01:04 So that is comparable to saying the probability of a history book followed by a history book, which when we reach in to find the first history book, there are two favorable books out of nine possible books.

01:23 And once we get one of those, now when we reach in, there's only one favorable book, and there's eight possible books in the locker at that time.

01:33 So when we multiply these out, you will get two over six.

01:37 Which is the same as 1 over 36 and as a decimal to the nearest thousandth would be 0 .028.

01:49 For question number two, we want the probability that both books are english books.

01:58 So that means the first book out will be an english book, and then the second book out would be an english book.

02:08 So this time when we reach in, there are three favorable books out of nine possible books.

02:16 We get one of those, so now there's eight books in the locker and two favorable books.

02:25 You will end up with six over 72, which is the same as one -twelfth, and as a decimal to the nearest thousandth would be .083.

02:39 For problem number three, we want the probability that one book is a math book and the other is a biology book.

02:47 So the probability of math and biology.

02:54 So that means we could get the math book first followed by the biology book, or we can get the biology book first followed by the math book.

03:11 So for the first probability, the probability of a math book is one out of nine.

03:19 And if we got that math book, then there are eight books left in the locker.

03:30 So when we reach for the biology book, it's one out of eight.

03:35 Or in probability means to add, and then if it's the other way around, we reach in, we get the biology book first, and then we go for the math book.

03:46 Well, there's one math book, but there's only eight books left in the locker.

03:49 So that would be one over 72, plus one over 72, or 2 over 72, which is the same as 1 out of 36, and as a decimal to the nearest thousandth would be 0 .028.

04:07 Number four, we're asking which is more likely, the probability of two french books or the probability of two english books? well, we already know the probability of two english books is 0 .083.

04:33 So let's do the probability of two french books.

04:36 So when we reach in and get the first french book out, it would be two out of nine.

04:43 When we reach in and get the second french book, well, now there's only one left and there's only eight books left.

04:51 So that would be two out of 72 or one out of 36.

04:56 Which is a probability of about 0 .08.

05:04 So therefore, the two english books is more likely because it's a higher probability.

05:16 Now, the next four problems involved in this problem involved the chart.

05:22 So we have this chart.

05:25 So i'm going to reproduce the chart...