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3 A card is drawn from a full pack of 52 playing cards. If the card drawn is an Ace, King, Queen or Jack, two dice are thrown and the sum of the scores on the dice noted. If any other card is drawn, one die only is thrown and the sum of the scores on the card and the die noted. X denotes the event 'Both dice are thrown', and Y denotes the event 'The score noted is less than five'. Calculate the probabilities: (a) P(X), (b) P(XY), (c) P(Y), (d) P (YX), (e) P(X|Y)

3 A card is drawn from a full pack of 52 playing cards. If the card drawn is an Ace, King, Queen or Jack, two dice are thrown and the sum of the scores on the dice noted. If any other card is drawn, one die only is thrown and the sum of the scores on the card and the die noted. X denotes the event 'Both dice are thrown', and Y denotes the event 'The score noted is less than five'. Calculate the probabilities: (a) P(X), (b) P(XY), (c) P(Y), (d) P (YX), (e) P(X|Y)

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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Calculate (a) P(XY), (b) P(YX), (c) P(XUY') A fair die is thrown three times. Events A, B C are defined as follows: A the total score is an odd number B a six appears at the first throw C the total score is 13. (a) Calculate P(A) and P (A | B) and state whether A and B are independent events Calculate P(C) and P (C|B) and state whether B and C are independent events. (b) 3 A card is drawn from a full pack of 52 playing cards. If the card drawn is an Ace, King, Queen or Jack, two dice are thrown and the sum of the scores on the dice noted. If any other card is drawn, one die only is thrown and the sum of the scores on the card and the die noted. X denotes the event 'Both dice are thrown', and Y denotes the event 'The score noted is less than five'. Calculate the probabilities: (a) P(X), (b) P(XY), (c) P (Y), (d) P (YX), (e) P(XY) A bottle of sweets contains 13 red sweets, 13 blue sweets, 13 green sweets and 13 yellow sweets.7 sweets are selected at random. Find the probability that exactly 3 of them are red. 5 Two fair twelve-sided dice with sides marked 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 are thrown, and the numbers on the sides which land face down are noted. Events Q and R are defined as follows. Q: the product of the two numbers is 24. R: both of the numbers are greater than 8. (i) Find P(Q). 2
Transcribed Image Text:Calculate (a) P(XY), (b) P(YX), (c) P(XUY') A fair die is thrown three times. Events A, B C are defined as follows: A the total score is an odd number B a six appears at the first throw C the total score is 13. (a) Calculate P(A) and P (A | B) and state whether A and B are independent events Calculate P(C) and P (C|B) and state whether B and C are independent events. (b) 3 A card is drawn from a full pack of 52 playing cards. If the card drawn is an Ace, King, Queen or Jack, two dice are thrown and the sum of the scores on the dice noted. If any other card is drawn, one die only is thrown and the sum of the scores on the card and the die noted. X denotes the event 'Both dice are thrown', and Y denotes the event 'The score noted is less than five'. Calculate the probabilities: (a) P(X), (b) P(XY), (c) P (Y), (d) P (YX), (e) P(XY) A bottle of sweets contains 13 red sweets, 13 blue sweets, 13 green sweets and 13 yellow sweets.7 sweets are selected at random. Find the probability that exactly 3 of them are red. 5 Two fair twelve-sided dice with sides marked 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 are thrown, and the numbers on the sides which land face down are noted. Events Q and R are defined as follows. Q: the product of the two numbers is 24. R: both of the numbers are greater than 8. (i) Find P(Q). 2
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