Three guests come to dinner, leaving their hats by the front door. When the time

Q: Three guests come to dinner, leaving their hats by the front door. When the time

a) The sample space for the given problem would be: {abc,acb,bac,bca,cab,cba} Therefore there are 6 elements in the sample space here. b) X is the random variable which represent the number of people who got their own hats. Therefore the possible values of X are 0,1,3 P(X=0) = 2/6 = 1/3 P(X=1) = 3/6 = 1/2 P(X=3) = 1/6 Sample space element X abc 3 acb 1 bac 1 bca 0 cab 0 cba 1

ID: 3173026 • Letter: T

Question

Three guests come to dinner, leaving their hats by the front door. When the time comes to leave, the host cannot remember which hat belongs to each person, and randomly gives one to each.

a) List the sample space for this experiment. Each outcome should be given as a triple of 3 letters, with the position representing the person and the letter representing the hat. For example bca indicates that Mr. A gets Mr. B's hat, Mr.B gets Mr.C's hat, and Mr.C gets Mr.A's hat.

b) Define the random vairable X, to be the number given to the correct owner. List the possible values for X, and give their probabilities.

Explanation / Answer

a) The sample space for the given problem would be:

{abc,acb,bac,bca,cab,cba}

Therefore there are 6 elements in the sample space here.

b) X is the random variable which represent the number of people who got their own hats.

Therefore the possible values of X are 0,1,3

P(X=0) = 2/6 = 1/3

P(X=1) = 3/6 = 1/2

P(X=3) = 1/6

Sample space element X abc 3 acb 1 bac 1 bca 0 cab 0 cba 1

Navigate

Three groups perform identical measurements to determine the enthalpy of combust

Three gunmen face each other in a duel. All are excellent marksmen so it is not

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

Three guests come to dinner, leaving their hats by the front door. When the time

Question

Explanation / Answer

Related Questions

Navigate