Problem 1 There are 2 coins, one a fair coin and one a 2-headed coin. One of the coins is chosen at random and flipped 4 times, and all 4 outcomes are heads. What is the conditional probability that...

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Problem 1 There are 2 coins, one a fair coin and one a 2-headed coin. One of the coins is chosen at random and flipped 4 times, and all 4 outcomes are heads. What is the conditional probability that the chosen coin was the 2-headed coin? Problem 2 A deck of 52 cards contains four aces. If the cards are shuffled and distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all four aces will be received by the same player? Problem 3 Suppose that a box contains r red balls and w white balls. Suppose also that balls are drawn from the box one at a time, at random, without replacement. (a) What is the probability that all r red balls will be obtained before any white balls are obtained? (b) What is the probability that all r red balls will be obtained before two white balls are obtained? Problem 4 Suppose that a family has exactly n children (n≥2). Assume that the probability that any child will be a girl is 1/2 and that all births are independent. Given that the family has at least one girl, determine the probability that the family has at least one boy. Problem 1 Show that, Problem 2 Three fair dice are independently rolled, with outcomes , , , find:X1 X2 X3 1) P ( + = )X1 X2 X2 + X3 2) P ( > + )X1 X2 X3 3) P ( + + )X1 X2 12X3 = Problem 3 A store accepts either Mastercharge or VISA credit cards; 2490 of its customers pass Mastercharge, 6190 of its customers pass VISA, and 1190 carry both. 1) What percent of customers pass credit cards that the store will accept? 2) What percent pass VISA cards but not Mastercharge cards? Problem 4 In a random poker hand, (five cards are chosen without replacement from a deck of 52), find the probability of “3 of a kind”. This means a hand consisting of (a,a,a,b,c) where a,b,c are distinct denominations. (There are 13 denominations, each having 4 suits.) Problem 5 In poker dice, 5 fair dice are independently rolled. A full house consists of outcomes (a,a,a,b,b), where a and b are distinct integers in {1,2,3,4,5,6}, and the a’s and b’s occur in any order. For example: (2,3,3,2,2) or (4,4,6,6,4) are full houses. Find the probability of a full house. Problem 6 5290 of the students in a certain college are women, 590 of the students in this college are majoring in Computer Science; 290 of the students are women majoring in computer science. If a student is selected at random, find the probability that: 1) The student is a woman given that the student is majoring in computer science. 2) The student is majoring in computer science given that the student is a woman. Problem 7 There are 2 coins, one a fair coin and one a 2-headed coin. One of the coins is chosen at random and flipped 4 times, and all 4 outcomes are heads. What is the conditional probability that the chosen coin was the 2-headed coin? Problem 8 A deck of 52 cards contains four aces. If the cards are shuffled and distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all four aces will be received by the same player? Problem 9 Suppose that a box contains r red balls and w white balls. Suppose also that balls are drawn from the box one at a time, at random, without replacement. (a) What is the probability that all r red balls will be obtained before any white balls are obtained? (b) What is the probability that all r red balls will be obtained before two white balls are obtained? Problem 10 Suppose that a family has exactly n children (n≥2). Assume that the probability that any child will be a girl is 1/2 and that all births are independent. Given that the family has at least one girl, determine the probability that the family has at least one boy.
Answered Same DayFeb 07, 2021

Answer To: Problem 1 There are 2 coins, one a fair coin and one a 2-headed coin. One of the coins is chosen at...

Aarti answered on Feb 08 2021
134 Votes
New Doc 2021-02-08 10.20.02
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