• Probability

  • Probability Basics
  • Stochastic Processes
  • Poisson Process
  • Birth Processes
  • Birth & Death processes
  • Queuing theory
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  • Epidemics
  • Wiener process
  • Stochastic Calculus

Multiplication of Probabilities

Consider this example, a dice is rolled once, what is the probability that the number shown is Even and is four?

So, this is the multiplication of probabilities.

Solution to the above problem
A dice is rolled, so all possible events are six {1,2,3,4,5,6}, even numbers are three {1,3,5}, and four is only one event {4}. Thus,

Hence,

SO REMEMBER:

for disjoint events
for joint events
for joint events
for disjoint events (for example, the probability that the number is even and 3 is 0, because it cannot happen).

RELATED PAGES
- Addition of Probabilities
- Multiplication of Probabilities