Download Probability of Independent Events

11-3 Probability of Multiple Events
Warm Up!
1. How many outcomes are there for rolling a die?
2. How many outcomes are there for tossing a coin?
3. How many outcomes are there for rolling a die and then tossing a coin?
4. Does the outcome from rolling a die affect the outcome of tossing a coin? Explain.
Vocabulary
Compound Event – Probabilities of two or more things happening at once.
Independent Events – When the outcome of one event does not affect the probability
of second event, the two events are independent.
Dependent Events – Two events are dependent if the occurrence of one event affects
the probability of the second event.
Algebra 2: Lesson 11-3 Probability of Multiple Events
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Example 1: Tell whether each event is independent or dependent.
a.) Earning grades on your tests and earning your final semester grade.
b.) Selecting a red apple and then a green apple from a bag of 6 red and 4 green
apples, if no apples are returned to the bag.
c.) Selecting a red apple and then a green apple from a bag of 6 red and 4 green
apples, if the first apple is returned to the bag before the next selection.
d.) Flipping a coin and pulling a card from a deck of cards.
Probability of Independent Events
For independent events A and B: P(A and B) = P(A)  P(B)
Algebra 2: Lesson 11-3 Probability of Multiple Events
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Example 2: Suppose you toss a coin and roll a die. Find the probability of getting
heads on the coin and ‘5’ on the die.
Example 3: Suppose you spin a spinner with the numbers 1, 2, 3, and 4, and pick a
card from a standard deck. Find the probability of spinning a ‘4’ and choosing a face
card.
Example 4: A bag contains 3 red marbles and 5 blue marbles. One marble is chosen at
random and then replaced. A second marble is drawn. Find P(red, then blue).
Probability of Dependent Events
For dependent events A then B: P(A, then B) = P(A)  P(B, after A)
Algebra 2: Lesson 11-3 Probability of Multiple Events
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Example 5: A bag contains three red marbles and five blue marbles. One marble is
chosen at random and is not replaced. A second marble is drawn. Find P(red, then
blue).
Example 6: There are five discs in a CD player. Disc 1 has 8 songs, disc 2 has 10
songs, disc 3 has 13 songs, disc 4 has 9 songs, and disc 5 has 10 songs. The player has
a “random” button that selects songs at random and does not repeat until all songs are
played. What is the probability that the first song is selected from disc 3 and then
second song is selected from disc 4?
Example 7: Two cards are drawn from a standard deck. The first card is not returned
to the deck before the second draw. Find P(face, then face).
Homework: pp. 708 – 709 =>9 – 15, 22 – 26, 31 – 34
Algebra 2: Lesson 11-3 Probability of Multiple Events
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