Using Addition with Probability
Use the following scenario to solve the following problems: A card is drawn from a standard 52 card deck. Tell whether events A and B are inclusive or mutually exclusive, and then find the probability.
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Hint:
Mutually exclusive events are events that cannot occur at the same time. If the events are mutually exclusive, use the formula: P(A or B) = P(A) + P(B)
Inclusive events are events that can occur at the same time. If the events are inclusive, use the formula: P(A or B) = P(A) + P(B) – P(A and B)
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| 1) Tell whether events A and B are inclusive or mutually exclusive, and then find the probability.
Click here to view the card deck.
A: The card is red.
B: The card is a 3.
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| 2) Tell whether events A and B are inclusive or mutually exclusive, then find the probability.
A: The card is a diamond or a club.
B: The card is not a diamond.
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| 3) Tell whether events A and B are inclusive or mutually exclusive, and then find the probability.
A: The card is an ace of diamonds.
B: The card is black.
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If the spinner show below is spun once, find the probability of each event in the following problems.
Hint: Determine whether the events are inclusive or mutually exclusive. Then use the correct formula.
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| Refer to the following scenario and diagram below to solve the following problems: A ski team with 14 members has eight (8) members who ski downhill, five (5) members who ski cross country, and seven (7) members who are jumpers. Some skiers participate in more than one event according to the overlapping regions in the Venn diagram. Find the probability of each event if a skier is selected at random. |
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Independent and Dependent Events
Refer to the following scenario to solve the following problems: A box contains six (6) red balls, nine (9) white balls, and five (5) blue balls. A ball is selected and then replaced. Then, a second ball is selected. Find the probability of each event.
Hint: Since the first ball that is selected is replaced before selecting the second ball, these are independent events.
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Refer to the following scenario to solve the following problems: A bag contains five (5) purple beads, three (3) green beads, and two (2) orange beads. Two consecutive draws are made from the box without replacing the first draw. Find the probability of each event.
Hint: Since the first ball that is selected is not replaced before selecting the second ball, these are dependent events.
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Refer to the following scenario to solve the following problems: A spinner that is divided into six (6) congruent regions, numbered “one” through “six”, is spun once. Let “A” be the event “odd” and “B” be the event “5”. Find each of the given probabilities.
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| 26) Joe said that if you roll a number cube 6 times, one of those rolls will be a 1. Was Joe correct? Why or why not.
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Review
For the following questions, find the theoretical probability of each event when rolling a standard 6 sided die.
Click here to review the unit content explanation for Probability: Fundamental Counting Principle, Permutations, Combinations.
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For the following problems, evaluate each expression.
Click here to review the unit content explanation for Probability: Fundamental Counting Principle, Permutations, Combinations.
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| 34) Extended Learning
Watch the following video, then write a five-sentence paragraph summarizing the video.
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| 35) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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