In a certain small town, 3 professional burglars are currently out of prison: Alex, Becky, and Carl. Alex has in the past committed 55% of the burglaries committed by the three, Becky 31%, and Carl the rest. But only 1/3 of Alex’s jobs are burglaries of a residence, while half of Becky’s are, and all of Carl’s are. a)What is the probability that the next burglary in town (if one of the three did it) is the burglary of a residence?b)Sure enough, a resident reports a home burglary. If one of the three did it, what is the probability Becky was guilty?

Answer explained below

Step-by-step explanation:

Alex has in the past committed 55% of the burglaries committed by the three, Becky 31%, and Carl the rest, hence

probability, P(Carl doing a burglary) = 1 - P(Alex or Becky doing a burglary)

= 1 - (0.55 + 0.31)

= 0.14

a) P(next burglary in town is the burglary of a residence) = P(Alex did a burglary of a residence) + P(Becky did a burglary of a residence) + P(Carl did a burglary of residence

= 0.55*1/3 + 0.31*0.5 + 0.14*1

= 0.4783

b)From  Bayes' Theorem: P(A | B) = P(A & B) / P(B)

Hence,

P(Becky | a resident reports a home burglary) = P(Becky did a burglary of a residence) / P(burglary of a residence)

= (0.31 * 0.5)/0.4783

= 0.3240

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation:

answer: 1722

step-by-step explanation:

given: the mass of saturn=

the mass of mercury=

the number of times the mass of saturn is greater than the mass of mercury

hence, the mass of saturn is 1722 times greater than the mass of mercury.