Multiplication rule for "AND"

0/1
Introduction
Lessons
  1. P(A and B) VS. P(A or B)

    P(A and B): probability of event A occurring and then event B occurring in successive trials.
    P(A or B):
    probability of event A occurring or event B occurring during a single trial.
0/5
Examples
Lessons
  1. Multiplication Rule for "AND"
    A coin is tossed, and then a die is rolled.
    What is the probability that the coin shows a head and the die shows a 4?
    1. Independent Events VS. Dependent Events
      1. One card is drawn from a standard deck of 52 cards and is not replaced. A second card is then drawn.
        Consider the following events:
        A = {the 1st1^{st} card is an ace}
        B = {the 2nd2^{nd} card is an ace}
        Determine:
        \cdot P(A)
        \cdot P(B)
        \cdot Are events A, B dependent or independent?
        \cdot P(A and B), using both the tree diagram and formula
      2. One card is drawn from a standard deck of 52 cards and is replaced. A second card is then drawn.
        Consider the following events:
        A = {the 1st1^{st} card is an ace}
        B = {the 2nd2^{nd} card is an ace}
        Determine:
        \cdot P(A)
        \cdot P(B)
        \cdot Are events A, B dependent or independent?
        \cdot P(A and B), using both the tree diagram and formula
    2. Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls.
      A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A;
      if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.
      1. What is the probability of selecting a green ball from Bag A?
      2. What is the probability of selecting a green ball?
    Free to Join!
    StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
    • Easily See Your Progress

      We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
    • Make Use of Our Learning Aids

      Last Viewed
      Practice Accuracy
      Suggested Tasks

      Get quick access to the topic you're currently learning.

      See how well your practice sessions are going over time.

      Stay on track with our daily recommendations.

    • Earn Achievements as You Learn

      Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
    • Create and Customize Your Avatar

      Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
    Topic Notes
    \cdot P(A and B): probability of event A occurring and then event B occurring in successive trials.

    \cdot P(B | A): probability of event B occurring, given that event A has already occurred.

    \cdot P(A and B) = P(A) \cdot P(B | A)

    \cdot Independent Events
    If the events A, B are independent, then the knowledge that event A has occurred has no effect on the probably of the event B occurring, that is P(B | A) = P(B).
    As a result, for independent events: P(A and B) = P(A) \cdot P(B | A)
    = P(A) \cdot P(B)