- Assume 60% of population have DVD and 35% have iPod. If someone is selected at random what is probability that they either have a DVD or iPod?
- In a factory, machines of type A produce 30% of the output, machines of type B produce 25%, and machines of type C produce 45% of the output. On average, 2% of the produce from the machines of type A is defective, with 3% defective from type B and 4% from type C. Calculate the probability that an item of output from the factory chose at random is defective. If a defective item is chosen calculate the probability that it was made by a machine of type C?
- The police discover a murder victim at 6:00am. The body temp of victim is measured then found to 28 deg C. A doctor arrives on the scene of the crime 60 minutes later and measures the body temp again. It is found to be 24 deg C. the temp of the room remains constant at 12 deg C. the doctor knowing that normal body temp is 37 deg C, is able to estimate the time of death of the victim. If the cooling process is modelled by the equation θ = θ
_{0 }е^{-kt}, where θ is the excess temp over room temperature, use this model to estimate the time of death.