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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