Statistics for Maintenance Modelling: Basic Probability Concepts

# Definition of Conditional Probability¤

The updated probability of event E given that a dependent event F has occurred is the conditional probability of E given F. The conditional probability is denoted P(E|F). The following definition holds for the conditional probability if P(F) > 0.

This says that the probability that event E occurs given event F has occurred is equal to the probability of event E or event F or both events E and F occurring divided by the probability of event F occurring.

If a coin is flipped twice and we assume that all four points in the sample space S = {(H, H), (H, T), (T, H), (T, T)} are equally likely, what is the conditional probability that both flips result in heads, given that the first flip does? Click on one of the options below, then click on "Check Answer".

1/4
1/2
3/4
Yes, the probability is 1/2. If E = {(H, H)} denoted the event that both flips land heads, and F = {(H, H), (H, T)} the event that the first flip lands heads, then the desired probability is given by:
No, the probability is actually 1/2. If E = {(H, H)} denoted the event that both flips land heads, and F = {(H, H), (H, T)} the event that the first flip lands heads, then the desired probability is given by: