A compound probability is how likely multiple events will happen. For
example, to calculate the probability of flipping heads,
and
then flipping heads again, multiply the probability of flipping heads
the first time by the probability of flipping heads the second time:
first probability = 0.5
second probability = 0.5
compound probability = 0.5 × 0.5 = 0.25 = 25%
In the example above, the probability of flipping heads is the same for
both flips. This is because they are independent events, meaning the
first flip does not influence the second flip. If instead you were to
draw colored marbles from a bag, and calculate the probability of
drawing a blue marble followed by another blue marble without putting
the first marble back, the probabilities would differ, because after
the first draw, there are now fewer blue marbles in the bag, making it
harder to draw another blue marble.
To calculate the probability of flipping heads
or flipping
tails with a single flip, add the probability of flipping heads and the
probability of flipping tails:
first probability = 0.5
second probability = 0.5
compound probability = 0.5 + 0.5 = 1 = 100%
In the example above, flipping heads and flipping tails are mutually
exclusive, meaning there is no overlap between the two events. Either
you flip heads, or you flip tails, both cannot happen. If instead you
were to calculate the probability of flipping heads on the first flip
or on the second flip, you would add the probability of
flipping heads the first time and the probability of flipping heads the
second time, and then subtract the probability of flipping heads on
both flips since that was double counted:
first probability = 0.5
second probability = 0.5
compound probability = 0.5 + 0.5 - (0.5 × 0.5) = 0.75 = 75%