Post on 23-Jun-2020
April 02, 2012
1. Bell Work: OAA Probability #2
2. Vocabulary: Ch. 10.5
3. Notes/Examples: Ch. 10.5
4. HW: WS Practice B 10.5
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Learn to find the probabilities of independent and dependent events.
compound eventsindependent eventsdependent events
VocabularyMath Book
page 545
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Skydivers carry two independent parachutes. One parachute is the primary parachute, and the other is for emergencies.
A compound event is made up of two or more separate events. To find the probability of a compound event, you need to know if the events are independent or dependent.
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Events are independent events if the occurrence of one event does not affect the probability of the other.
Events are dependent events if the occurrence of one does affect the probability of the other.
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Determine if the events are dependent or independent.
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Determine if the events are dependent or independent.
A. getting tails on a coin toss and rolling a 6 on a number cube
B. getting 2 red gumballs out of a gumball machine
Tossing a coin does not affect rolling a number cube, so the two events are independent.
After getting one red gumball out of a gumball machine, the chances for getting the second red gumball have changed, so the two events are dependent.
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An experiment consists of spinning the spinner 3 times.
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An experiment consists of spinning the spinner 3 times.
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An experiment consists of spinning the spinner 3 times.
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Three separate boxes each have one blue marble and one green marble. One marble is chosen from each box.
What is the probability of choosing a blue marble from each box?
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What is the probability of choosing a blue marble, then a green marble, and then a blue marble?
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What is the probability of choosing at least one blue marble?
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To calculate the probability of two dependent events occurring, do the following:
1. Calculate the probability of the first event.2. Calculate the probability that the second event would occur if the first event had already occurred.3. Multiply the probabilities.
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A jar contains 16 quarters and 10 nickels.If 2 coins are chosen at random, what is the probability of getting 2 quarters?
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A jar contains 16 quarters and 10 nickels.If 2 coins are chosen at random, what is the probability of getting 2 coins that are the same?
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Two mutuallyexclusive events
cannot both happenat the same time.
Remember
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The letters in the word dependent are placed in a box.If two letters are chosen at random, what is the probability that they will both be consonants?
Because the first letter is not replaced, the sample space is different for the second letter, so the events are dependent. Find the probability that the first letter chosen is a consonant.
If the first letter chosen was a consonant, now there would be 5 consonants and a total of 8 letters left in the box. Find the probability that the second letter chosen is a consonant
The probability of choosing two letters that are both consonants is 5
12
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If two letters are chosen at random, what is the probability that they will both be consonants or both be vowels?There are two possibilities: 2 consonants or 2 vowels. The probability of 2 consonants was calculated in Example 3A. Now find the probability of getting 2 vowels.
Find the probability that the first letter chosen is a vowel.
If the first letter chosen was a vowel, there are now only 2 vowels and 8 total letters left in the box.
Find the probability that the second letter chosen is a vowel.
Multiply.The events of both consonants and both vowels are mutually exclusive, so you can add their probabilities.
P(consonant) + P(vowel)The probability of getting two letters that are either both consonants or both vowels is .1
2
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Are you having trouble deciding when to add probabilities and when to multiply them.
When outcomes are separated by the word or, their probabilities are usually added (e.g., rolling a 4 or a 5 on a number cube).
When outcomes are separated by and, their probabilities are usually multiplied (e.g., drawing a red marble and a blue marble out of a bag).
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Compete page 548
#1-11
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