Question

An epidemiologist is modelling a random variable describing the time that it takes for an outbreak to double in size. In the resulting random trial, the occurrence of the event A = "the outbreak has not yet doubled in size after two weeks" implies that the event B = "the outbreak has not yet doubled in size after one week" must also occur. Which of these events must have a larger probability? Explain.

Answer 1

An epidermologist is modelling a random variable describing the time it takes for an outbreak to double in size.

Event A is " the outbreak has not yet doubled in size after two weeks " implies that the Event B " the outbreak has not yet doubled in size after one weeks ", must occur

Now, A implies B. This means that

P(B|A)=1

By the definition of conditional probability,

this means

So, as A is the event in the intersection of A and B, A must be the smaller event.

So, B should have the higher probability.

So, the event that the outbreak has not yet doubled in size after one week, ie. B has larger probability.