19.4 Mutually Exclusive and Overlapping Events Date: ______
Mutually Exclusive Events
Learning Target G: I can find the probability of Mutually Exclusive and Overlapping events.
Mutually Exclusive EventsTwo events are mutually exclusive events if they cannot both occur in the same trial of an experiment.
Example) a coin cannot land heads up and tails up in the same trial
Tell whether each pair of events is mutually exclusive.
1. Rolling a 5 and rolling an even number on a number cube.
2. Drawing an Ace and drawing a diamond from a standard deck of cards.
3. From a bag of marbles, drawing a yellow marble and drawing a red marble.
4. Drawing a face card and drawing an odd number from a standard deck of cards.
Finding the Probability of Mutually Exclusive Events.
When events are mutually exclusive, they have no outcomes in common. Because of this, when we are finding the probability mutually-exclusive events A and B, we can simply ______their individual probabilities together.
Probability of Mutually Exclusive EventsIf A and B are mutually exclusive events, then PA or B=PA+P(B)
Given a standard deck of playing cards, find each probability.
1. Drawing an ace or a face card.
2. Drawing a red card or a black 10.
3. Drawing a King or and even number.
4. Drawing a face card or a seven
Overlapping Events
Overlapping EventsTwo events are overlapping (or inclusive events) if they have one or more outcomes in common.
Because overlapping events have outcomes in common, we cannot just add their probabilities together. We need to identify the overlapping outcomes and subtract them.
The Addition Rule – Overlapping EventsPA or B=PA+PB-P(A and B)
Given a regular 6-sided die, find each probability.
1. Rolling an even number or rolling a number less than 4.
2. Rolling a number greater than 3 or rolling an even.
3. Rolling an odd number or rolling a number greater than 1.
Given a standard deck of playing cards, find each probability.
4. P(drawing a spade or drawing a seven).
5. P(drawing a face card or drawing a black card).
20.2 and 20.3 Independent and Dependent Events
Explore- Understanding the Independence of Events
Suppose you flip a coin and roll a number cube. You would expect the probability of getting heads on the coin to be 12 regardless of what you get from rolling the number cube. Likewise, you would expect the probability of rolling a 3 on the number cube to be 16 regardless of the coin flip results in heads or tails.
When the occurrence of one event has no effect on the occurrence of another event, the two events are called independent events.
A jar contains 15 red marbles and 17 yellow marbles. You randomly draw a marble from the jar. Let R be the event that you get a red marble, and let Y be the event that you get a yellow marble.
A) Find P(R) and P(Y).
B) Suppose the first marble you draw is a red marble, and you put that marble back in the jar before randomly drawing a second marble. Find the probability that you get a yellow marble on the second draw after getting a red marble on the first draw. Explain.
C) Suppose you do not put the red marble back into the jar before randomly drawing a second marble. Find the probability that you get a yellow marble on the second draw after getting a red marble on the first draw. Explain your reasoning.
D) In one case you replaced the first marble before drawing the second, and in the other case you didn’t. In which of the two cases would you say that the events of getting a red marble on the first draw and getting a yellow marble on the second draw are independent?
Finding the Probability of Two Dependent Events
Learning Target H: I can determine the probability of two dependent events.
You can use the Multiplication Rule to find the probability of dependent events.
There are 5 tiles with the letters A, B, C, D, and E in a bag. You choose a tile without looking, put it aside, and then choose another tile without looking. Use the Multiplication Rule to find the specified probability, writing it as a fraction.
A) Find the probability that you choose a vowel followed by a consonant.
B) Find the probability that you choose a vowel followed by another vowel.
A bag holds 4 white marbles and 2 blue marbles. You choose a marble without looking, put it aside and then choose another marble without looking. Use the Multiplication Rule to find the specified probability, writing it as a fraction.
A) Find the probability that you choose a white marble followed by a blue marble.
B) Find the probability that you choose a white marble followed by another white marble.