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8. A bag contains 7 red marbles, 8 green marbles and 10 blue marbles. Five marbles are randomly drawn from the bag. (a) If it's known that the first two of the marbles are blue, what is the probability that the other three marbles are red? (b) If it's known that the first marble is green, what is the probability that the last marble is also green? (c) If it's known that none of the marbles are red, what is the probability that there are more green marbles than blue marbles? (d) If it's known that there are the same numbers of red and green marbles, what is the probability that only one of the marbles is blue?

8. A bag contains 7 red marbles, 8 green marbles and 10 blue marbles. Five marbles are randomly drawn from the bag. (a) If it's known that the first two of the marbles are blue, what is the probability that the other three marbles are red? (b) If it's known that the first marble is green, what is the probability that the last marble is also green? (c) If it's known that none of the marbles are red, what is the probability that there are more green marbles than blue marbles? (d) If it's known that there are the same numbers of red and green marbles, what is the probability that only one of the marbles is blue?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please help me with question #8 with as much explanation as possible please. I really want to understand this
= .7 and P(B) = .65 2. (a) Assume P(A) = .64, P(B) = .48 and P(An B) = .33. Find P(A U B), P(An BC) and P(A U BC). (b) Assume P(A U B) = .87 and P(A U BC) = .63. Find P(A). 3. (a) Show that P(A-B) + P(B-A)=P(AUB) - P(An B). (b) Show that P(A U BUC) = P(A) + P(B) + P(C) - P(An B)- P(ANC) - P(BNC) + P(An BnC). 4. Tom is currently taking an English reading class and an English writing class. He estimates that the chance he will pass each class is 60% and 80%, respectively. And he also estimates that the chance he will fail both classes is 15%. Assume his estimation is correct. (a) What is the probability that Tom will pass both classes? (b) What is the probability that Tom will pass only one of the classes? (c) If it's known that Tom passes his reading class, what is the probability that he also passes his writing class? (d) If it's known that Tom fails his reading class, what is the probability that he also fails his writing class? 5. Given a set of digits (0, 1,3,5,6, 8, 9), and a four-digit-number is formed using the digits in the set without repetition. (Note: A four-digit-number cannot start with a "0".) (a) What is the probability that the number is even? (b) What is the probability that the number is odd and greater than 5000? (c) What is the probability that the number is less than 5600? (d) If it's known that the number is even, what is the probability that it's greater than 5000? 6. A hand of 5 cards is dealt to each of three players from a standard deck of 52 cards. (a) What is the probability that at least one player receive at least one heart? (b) What is the probability that at least one player receive five hearts? (c) What is the probability that at least one player receive exactly two hearts? (d) What is the probability that at least two players receive exactly two hearts? 7. A hand of 6 cards is drawn from a standard 52 card deck. (a) What is the probability of getting three different pairs? (ex: aabbcc) (b) What is the probability of getting two pairs? (ex: aabbcd) (c) What is the probability of getting three of a kind? (ex: aaabcd) (d) What is the probability of getting all cards with the same suit? 8. A bag contains 7 red marbles, 8 green marbles and 10 blue marbles. Five marbles are randomly drawn from the bag. (a) If it's known that the first two of the marbles are blue, what is the probability that the other three marbles are red? (b) If it's known that the first marble is green, what is the probability that the last marble is also green? (c) If it's known that none of the marbles are red, what is the probability that there are more green marbles than blue marbles? (d) If it's known that there are the same numbers of red and green marbles, what is the probability that only one of the marbles is blue? 9. John is currently taking a calculus class, and he will have a test next week. He estimates that if he studies over the weekend, he will have 70% chance to pass the test, and if he doesn't study over the weekend, he only has 20% chance to pass the test. Assume John's estimation is correct, and John has a 90% chance to study over the weekend. (a) What is the probability that John will pass the test? (b) If it's known that John passes the test, what is the probability that he doesn't study over the weekend? (c) If it's known that John fails the test, what is the probability that he studies over the weekend? 10. Box A has 3 green marbles and 1 red marble, box B has 4 green marbles and 2 red marbles, and box C has 5 green marbles and 3 red marbles. Peter rolls a die first. If the die comes up 1, then he will randomly choose a marble from box A; if the die comes up 2 or 3, he will randomly choose a marble from box B; if the die comes up 4, 5 or 6, he will randomly choose a marble from box C. (a) What is the probability that Peter gets a red marble? (b) If it's known that Peter gets a red marble, what is the probability that the marble is chosen from box A? (c) If it's known that Peter gets a green marble, what is the probability that the marble is chosen from box C?
Transcribed Image Text:= .7 and P(B) = .65 2. (a) Assume P(A) = .64, P(B) = .48 and P(An B) = .33. Find P(A U B), P(An BC) and P(A U BC). (b) Assume P(A U B) = .87 and P(A U BC) = .63. Find P(A). 3. (a) Show that P(A-B) + P(B-A)=P(AUB) - P(An B). (b) Show that P(A U BUC) = P(A) + P(B) + P(C) - P(An B)- P(ANC) - P(BNC) + P(An BnC). 4. Tom is currently taking an English reading class and an English writing class. He estimates that the chance he will pass each class is 60% and 80%, respectively. And he also estimates that the chance he will fail both classes is 15%. Assume his estimation is correct. (a) What is the probability that Tom will pass both classes? (b) What is the probability that Tom will pass only one of the classes? (c) If it's known that Tom passes his reading class, what is the probability that he also passes his writing class? (d) If it's known that Tom fails his reading class, what is the probability that he also fails his writing class? 5. Given a set of digits (0, 1,3,5,6, 8, 9), and a four-digit-number is formed using the digits in the set without repetition. (Note: A four-digit-number cannot start with a "0".) (a) What is the probability that the number is even? (b) What is the probability that the number is odd and greater than 5000? (c) What is the probability that the number is less than 5600? (d) If it's known that the number is even, what is the probability that it's greater than 5000? 6. A hand of 5 cards is dealt to each of three players from a standard deck of 52 cards. (a) What is the probability that at least one player receive at least one heart? (b) What is the probability that at least one player receive five hearts? (c) What is the probability that at least one player receive exactly two hearts? (d) What is the probability that at least two players receive exactly two hearts? 7. A hand of 6 cards is drawn from a standard 52 card deck. (a) What is the probability of getting three different pairs? (ex: aabbcc) (b) What is the probability of getting two pairs? (ex: aabbcd) (c) What is the probability of getting three of a kind? (ex: aaabcd) (d) What is the probability of getting all cards with the same suit? 8. A bag contains 7 red marbles, 8 green marbles and 10 blue marbles. Five marbles are randomly drawn from the bag. (a) If it's known that the first two of the marbles are blue, what is the probability that the other three marbles are red? (b) If it's known that the first marble is green, what is the probability that the last marble is also green? (c) If it's known that none of the marbles are red, what is the probability that there are more green marbles than blue marbles? (d) If it's known that there are the same numbers of red and green marbles, what is the probability that only one of the marbles is blue? 9. John is currently taking a calculus class, and he will have a test next week. He estimates that if he studies over the weekend, he will have 70% chance to pass the test, and if he doesn't study over the weekend, he only has 20% chance to pass the test. Assume John's estimation is correct, and John has a 90% chance to study over the weekend. (a) What is the probability that John will pass the test? (b) If it's known that John passes the test, what is the probability that he doesn't study over the weekend? (c) If it's known that John fails the test, what is the probability that he studies over the weekend? 10. Box A has 3 green marbles and 1 red marble, box B has 4 green marbles and 2 red marbles, and box C has 5 green marbles and 3 red marbles. Peter rolls a die first. If the die comes up 1, then he will randomly choose a marble from box A; if the die comes up 2 or 3, he will randomly choose a marble from box B; if the die comes up 4, 5 or 6, he will randomly choose a marble from box C. (a) What is the probability that Peter gets a red marble? (b) If it's known that Peter gets a red marble, what is the probability that the marble is chosen from box A? (c) If it's known that Peter gets a green marble, what is the probability that the marble is chosen from box C?
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