Joint Probability

A joint probability is simply the likelihood that two random events happen at the same time. Not to be confused with a conditional probability, which is the probability that one event happens following the occurrence of another.

In general, if we want to know the probability that two events (A and B) happen at the same time, we just multiply their individual probabilities (P(A) and P(B)) together. Luckily, the only real condition we need to make sure we’ve met is checking to see that both events can actually happen at the same time. If they can’t happen at the same time, that makes the joint probability that they both happen equal to zero.

Let’s say we’re following two stocks that we’re kinda, maybe, sorta interested in. Data shows that there’s a 25% chance that Fred’s Burgers stock will gain in price in a given month, while there’s a 30% chance that Reaper’s Sewing Machines will gain price in a given month. If we’re interested in the probability that they both gain value in the same month, we just take each individual probability (0.25 and 0.3) and give them a good swift multiplying. 0.25 × 0.3 = 0.075, or about a 7.5% probability that they both experience a price gain.

Since that pizza place thing is a no-go, we’re hoping the joint probability that we get a Starbucks and a Subway in the strip mall one block over is something north of 99%.