Part B Complete the following questions using R and R commander. 1. People can be right handed, mixed handed, or left handed: RH, MH, LH. People can also be right footed,

mixed footed or left footed: RF, MF, LH. So a person can be one of 9 handedfooted possibilities: RHRF, RHMF, RHLF, MHRF, MHMF, MHLF, LHRF, LHMF, LHLF. Table 3 in the 2016 research paper "Footedness Is Associated with Self-reported Sporting Performance and Motor Abilities in the General Population", by Ulrich S. Tran and Martin Voracek summarizes a study of handedness and footedness in 12720 people. https://www.frontiersin.org/articles/10.3389/fpsyg.2016.01199/full. The dataset TRANVORACEKHANDFOOT contains raw data from which the following two way table of counts for the 9 cells RHRF, RHMF, RHLF, MHRF, MHMF, MHLF, LHRF, LHMF, LHRF can be obtained. Your instructor added the totals. LH MH RH TOTALS LF 602* 45 396 1043 MF 247 219 3373 3839 RF 177 33 7628 7838 TOTALS 1026 297 11397 12720 (a) Check that you can get the results of the table of Tran and Voracek by generating a two- way table in R from the TRANVORACEKHANDFOOT dataset. Paste your result. (3 marks) (b) Find, by hand, the probability that a randomly selected person is left handed. (2 marks) STAT 151 (c) Find, by hand, the probability that a randomly selected person is left handed and right footed. (2 marks) (d) Find, by hand, the probability that a randomly selected person is left handed or right footed. (3 marks) (e) Find, by hand, the probability that a randomly selected left-handed person is mixed footed. That is, find the probability that a randomly selected person is mixed-footed given they are left-handed. (3 marks) (f) Find, by hand, the probability that a randomly selected mixed-footed person is left- handed. (3 marks) (g) Are events MF and LH independent? Explain your answer by hand. (2 marks) (h) Are events LH and MF mutually exclusive? Explain your answer by hand. (2 marks) 5