The following table contains a break-down on the age and gender of mid-level managers in one company in Toronto. Age in years under 35 35-44 45-54 55-64 over 64 Total Male 15 12 19 10 Female 5 12 34 Total 7 29 17 21 22 96 Round all final answers to 3 decimal places and express probabilities in decimal form (ie. 0.003 instead of 0.300%). (a) What is the probability that a randomly selected manager is 35-44 years old? (b) What is the probability that a randomly selected manager is a female? (c) What is the probability that a randomly selected manager is a female and 35-44 years old? (d) What is the probability that a randomly selected manager is a female or 35-44 years old? (2) What is the probability that a randomly selected manager is neither female, nor 35- 44 years old?DO IDEAS X C An Insurance Company Survey'S x + C imathas.humber.ca/assess2/?cid=494&laid=14671#/skip/1 Apps YouTube Maps Gmail Google Microsoft Office Ho.. OO Statistics class IDEAS (f) What is the probability that a randomly selected manager is a female given that the manager is 35-44 years old? (g) What is the probability that a randomly selected manager is 35-44 years old given that the manager is a female?An insurance company survey shows that 88% of all Ontario drivers wear seatbelt. For those who wear seatbelt, it is estimated that the chance of getting a serious injury in a car accident is 8%. For those who do not wear a seatbelt, the chance of getting a serious injury is 74%. If S represents the event of wearing a seatbelt, NVS is the event of not wearing a seatbelt, I is the event of serious injury, and NV/ is the event of not sustaining a serious injury, then answer the following questions: Searbeals Injury NI NI a Round all final answers to 4 decimals. (a) Fill in the probability tree values: (1) (1i)(iii): (iv): (u): (vi): (b) Write down the results of your probability tree diagram below: P(S and I) = P(S and NI) = P(NS and ]) = P(NS and NI) = (c) If in a randomly selected car accident the driver was seriously hurt, the probability that the driver was not wearing seatbelt is (d) If in a randomly selected car accident the driver was not seriously hurt, the probability that the driver was wearing seatbelt is