Probability of independent events

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Introduction
Lessons
  1. Differences between independent events and dependent events
  2. Addition and multiplication rules for probability
  3. Experimental probability VS. Theoretical probability
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Examples
Lessons
  1. A spinner divided in 4 equal sections is spun. Each section of the spinner is labeled 1, 2, 3, and 4. A marble is also drawn from a bag containing 5 marbles: one green, one red, one blue, one black, and one white. Find the probability of:
    1. Landing on section 2 and getting the green marble.
    2. Not landing on section 3 and not getting the black marble.
    3. Landing on section 1 or 4 and getting the red or blue marble.
    4. Landing on any section and getting the white marble.
  2. A coin is flipped, a standard six-sided die is rolled; and a spinner with 4 equal sections in different colours is spun (red, green, blue, yellow). What is the probability of:
    1. Getting the head, and landing on the yellow section?
    2. Getting the tail, a 6 and landing on the red section?
    3. Getting the tail, a 2 and not landing on the blue section?
    4. Not getting the tail; not getting a 3; and not landing on the blue section?
    5. Not getting the head; not getting a 5; and not landing on the green section?
  3. A toy vending machine sells 5 types of toys including dolls, cars, bouncy balls, stickers, and trains. The vending machine has the same number of each type of toys, and sells the toys randomly. Don uses a five-region spinner to simulate the situation. The results are shown in the tall chart below:

    Doll

    Car

    Bouncy Ball

    Sticker

    Train

    ||||

    ||||

    |||

    ||

    ||

    1. Find the experimental probability of P(doll).
    2. Find the theoretical probability of P(doll).
    3. Compare the experimental probability and theoretical probability of getting a doll. How to improve the accuracy of the experimental probability?
    4. Calculate the theoretical probability of getting a train 2 times in a row?
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Topic Notes
Probability is everywhere in our daily life. Do you know your chances of winning a specific prize in a spinning wheel prize draw? How about the odd to get the same prize two times in a row? By applying the concept of probability of independent events, we can easily answer these questions.