Question

From the 2012 census, we know that 50.8% of the us population is female. In addition, 667039 men and 93 176 females are in jail. B) let m denote the events that someone is male. Let j denote the events that someone is in jail. Without actually calculating the conditional propabilities, predict whether the two calculations P(m/j) and P(j/m) are likely to be similar or different in this context.

Answer 1

The probability that a person is male if he is in jail, P(m/j), is high (far above 50%), since the given shows that there are more than 600,000 men while less than 100,000 women in jail. On the other hand, the probability that a person is in jail if he is a male, P(j/m), is fairly low, since far less than 50% of males are in jail. Therefore, these are likely to be different.