Probstat/week2 practice 1 - ประวัติรุ่นแก้ไข

Jittat: /* Counting */

2014-09-04T07:09:57Z

Counting

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2014-08-28T03:07:00Z

Counting

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2014-08-28T02:55:58Z

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2014-08-26T07:07:05Z

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2014-08-26T07:06:45Z

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2014-08-26T07:05:50Z

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Jittat: /* Counting */

2014-08-26T07:01:50Z

Counting

Jittat เมื่อ 07:01, 26 สิงหาคม 2557

2014-08-26T07:01:30Z

Jittat: /* Conditional probability review */

2014-08-26T06:59:23Z

Conditional probability review

Jittat: /* Counting */

2014-08-26T06:58:41Z

Counting

@@ แถว 69: / แถว 69: @@
 * 9.2 In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are to sit together?
 * 9.3 In how many ways can 3 boys and 3 girls sit in a row if only the boys are to sit together?
-* 9.3 In how many ways can 3 boys and 3 girls sit in a row if no two people of the same gender are allowed to sit together?
+* 9.4 In how many ways can 3 boys and 3 girls sit in a row if no two people of the same gender are allowed to sit together?
 . '''Poker.'''  (See [http://en.wikipedia.org/wiki/List_of_poker_hands wikipedia]) We have standard 52 cards with 4 suits (spades, hearts, diamonds, and clubs).  Each suit contains 13 cards: A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2.  A poker hand contains 5 cards.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:07, 28 สิงหาคม 2557
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	* 9.3 In how many ways can 3 boys and 3 girls sit in a row if only the boys are to sit together?		* 9.3 In how many ways can 3 boys and 3 girls sit in a row if only the boys are to sit together?
	* 9.3 In how many ways can 3 boys and 3 girls sit in a row if no two people of the same gender are allowed to sit together?		* 9.3 In how many ways can 3 boys and 3 girls sit in a row if no two people of the same gender are allowed to sit together?
		+
		+	10. '''Poker.''' (See [http://en.wikipedia.org/wiki/List_of_poker_hands wikipedia]) We have standard 52 cards with 4 suits (spades, hearts, diamonds, and clubs). Each suit contains 13 cards: A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2. A poker hand contains 5 cards.
		+
		+	* 10.1 How many different poker hands are there?
		+	* 10.2 How many different poker hands are there that do not contain ''any'' pair?
		+	* 10.3 How many different poker hands are there that contain at least one pair?
		+	* 10.4 How many different poker hands are there that are straight? (A straight is a hand that contains five cards of sequential rank)
		+	* 10.5 How many different poker hands are there that are straight flush? (A straight is a hand that contains five cards of sequential rank)

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	8. (From FCP, Ch1. Problems 2) Alice, Bob, Cathy, and Dave is forming a band that plays 4 instruments. If each member can play any instruments, how many different arrangements are possible? If Alice and Bob can play any instruments but Cathy and Dave can each play only piano and drums, how many different arrangements are possible?		8. (From FCP, Ch1. Problems 2) Alice, Bob, Cathy, and Dave is forming a band that plays 4 instruments. If each member can play any instruments, how many different arrangements are possible? If Alice and Bob can play any instruments but Cathy and Dave can each play only piano and drums, how many different arrangements are possible?
		+
		+	: ''These problems are added on Aug28.''
		+
		+	9. (From FCP, Ch1. Problems 4)
		+
		+	* 9.1 In how many ways can 3 boys and 3 girls sit in a row?
		+	* 9.2 In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are to sit together?
		+	* 9.3 In how many ways can 3 boys and 3 girls sit in a row if only the boys are to sit together?
		+	* 9.3 In how many ways can 3 boys and 3 girls sit in a row if no two people of the same gender are allowed to sit together?

@@ แถว 49: / แถว 49: @@
 . How many different letter arrangements can be formed from the following words
-* 5.1 '''PROBABILITY'''
+* 5.1 PROBABILITY
-* 5.2 '''KASETSART'''
+* 5.2 KASETSART
 . There are 5 female and 4 male students in a class.  We would like to pick 4 students as representatives.

@@ แถว 48: / แถว 48: @@
 . (From FCP, ex 3c) There are 4 different math books, 3 different history books, 2 different chemistry books, and 1 literature book.  We want to put these books in a shelf so that books from the same subject are together on the shelf.  How many ways to do that?
-. How many different letter arrangements can be formed from the word '''PROBABILITY'''?
+. How many different letter arrangements can be formed from the following words
 . There are 5 female and 4 male students in a class.  We would like to pick 4 students as representatives.

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 07:05, 26 สิงหาคม 2557
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	7. We would like to assign ID's to students' labtops. An ID is a 4-character string consisting of alphabets A, B, C, D, E, and F, that satisfies the conditions that (1) each alphabet appears at most once and (2) the string only contains at most one vowel. How many different ID's are there?		7. We would like to assign ID's to students' labtops. An ID is a 4-character string consisting of alphabets A, B, C, D, E, and F, that satisfies the conditions that (1) each alphabet appears at most once and (2) the string only contains at most one vowel. How many different ID's are there?
		+
		+	8. (From FCP, Ch1. Problems 2) Alice, Bob, Cathy, and Dave is forming a band that plays 4 instruments. If each member can play any instruments, how many different arrangements are possible? If Alice and Bob can play any instruments but Cathy and Dave can each play only piano and drums, how many different arrangements are possible?

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 07:01, 26 สิงหาคม 2557
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	* 6.3 If we want a set of representatives to consists of students from two different genders, how many different sets of representatives are possible?		* 6.3 If we want a set of representatives to consists of students from two different genders, how many different sets of representatives are possible?

−	7. We would like to assign ID to students' ~~labtop~~. An ID is a 4-character string consisting of alphabets A, B, C, D, E, and F, that satisfies the conditions that (1) each alphabet appears at most once and (2) the string only contains at most one vowel. How many different ID's are there?	+	7. We would like to assign ID's to students' labtops. An ID is a 4-character string consisting of alphabets A, B, C, D, E, and F, that satisfies the conditions that (1) each alphabet appears at most once and (2) the string only contains at most one vowel. How many different ID's are there?

@@ แถว 5: / แถว 5: @@
 . Consider a sample space <math>S = \{ 0,1,2,3,...,41 \}</math>. We randomly pick an integer from <math>S</math>.
-.1 What is the probability that a random number from <math>S</math> is divisible by 2 given that it is divisible by 3.
+* 1.1 What is the probability that a random number from <math>S</math> is divisible by 2 given that it is divisible by 3.
+* 1.2 Are events "an integer divisible by 2 is picked" and "an integer divisible by 3 is picked" independent?
-.2 Are events "an integer divisible by 2 is picked" and "an integer divisible by 3 is picked" independent?
+* 1.3 What is the probability that a random number from <math>S</math> is divisible by 4 given that it is divisible by 3.
+* 1.4 Are events "an integer divisible by 4 is picked" and "an integer divisible by 3 is picked" independent?
 . The following table shows probabilities of events related to people having lung cancer and smoking cigarette.   (Numbers are made up).
@@ แถว 31: / แถว 28: @@
 |}
-.1 What is the probability that a person has lung cancer if that person smokes?
+* 2.1 What is the probability that a person has lung cancer if that person smokes?
+* 2.2 What is the probability that a person does not have lung cancer if that person does not smokes?
-.2 What is the probability that a person does not have lung cancer if that person does not smokes?
+* 2.3 What is the probability that a person smokes if that person has lung cancer?
+* 2.4 A stupid cancer predictor works like this: it asks a person if that person smokes, if the person answers yes, the predictor predicts that the person has lung cancer.  Otherwise, the predictor predicts that the person does not have lung cancer.  What is the probability that the predictor is wrong?  (More precisely, suppose that we pick a random person, what is the probability that the predictor gives incorrect prediction?)
 == Counting ==

@@ แถว 60: / แถว 60: @@
 * 6.1 How many different sets of representatives are possible?
 * 6.2 If we want a set of representatives to consists of 2 female and 2 male students, how many different sets of representatives are possible?
+. We would like to assign ID to students' labtop.  An ID is a 4-character string consisting of alphabets A, B, C, D, E, and F, that satisfies the conditions that (1) each alphabet appears at most once and (2) the string only contains at most one vowel.  How many different ID's are there?
 == Permutations and combinations ==
 == Exercises ==