Exercise 4 - Calculate the Probability
Assume that the probability of a murderer finding a way to kill her two children without leaving evidence of physical harm is:
\(\mbox{Pr}(\mbox{two children found dead with no evidence of harm} \mid \mbox{mother is a murderer} ) = 0.50\)
Assume that the murder rate among mothers is 1 in 1,000,000.
\(\mbox{Pr}(\mbox{mother is a murderer} ) = 1/1,000,000\)
According to Bayes' rule, what is the probability of:
$$\mbox{Pr}(\mbox{mother is a murderer} \mid \mbox{two children found dead with no evidence of harm})$$
This exercise is part of the course
HarvardX Data Science Module 4 - Inference and Modeling
Exercise instructions
- Use Bayes' rule to calculate the probability that the mother is a murderer, considering the rates of murdering mothers in the population, the probability that two siblings die of SIDS, and the probability that a murderer kills children without leaving evidence of physical harm.
- Print your result to the console.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Define `Pr_1` as the probability of the first son dying of SIDS
Pr_1 <- 1/8500
# Define `Pr_2` as the probability of the second son dying of SIDS
Pr_2 <- 1/100
# Define `Pr_B` as the probability of both sons dying of SIDS
Pr_B <- Pr_1*Pr_2
# Define Pr_A as the rate of mothers that are murderers
Pr_A <- 1/1000000
# Define Pr_BA as the probability that two children die without evidence of harm, given that their mother is a murderer
Pr_BA <- 0.50
# Define Pr_AB as the probability that a mother is a murderer, given that her two children died with no evidence of physical harm. Print this value to the console.