Learning Task on Probability (Page 1) Name______
Suppose there is a game involving a deck of eight cards. For this task, make the deck of eight cards using the packet given to you by placing eight cards with the following values on your desk:
{1, 2, 3, 5, 6, 8, 10, 12}.
1. A person will randomly draw one card from the deck. How many different cards could
he/she possibly draw?
The answer to Question 1 is of the utmost importance because it represents the total number of outcomes when a person draws one card from the deck. Consider the following formula:
Probability =
Suppose one is working through probability problems in which a person will randomly draw one card from this deck.
2. The answer to Question 1 will serve as which of the following in every such probability
problem: the numerator of the answer or the denominator of the answer?
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As you work through the problems below, pick up the cards that do not meet the following criteria. Thus, the cards left on the desk would be all of the desired outcomes.
For Questions 3-5, suppose Nancy is randomly drawing one card from this deck.
3. What is the probability that Nancy draws a card with an even number? To help find the
number of desired outcomes, pick up any cards that do not have an even number.
4. What is the probability that Nancy draws a card with a number greater than 5?
5. What is the probability that Nancy draws a card with a number that is not equal to 5?
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While the concepts of mutually exclusive and not mutually exclusive events are very important, one can still just rely on the probability formula given above for problems involving both types of events.
6. Consider Questions 7-9. Which questions involve events that are mutually exclusive?
Remember - mutually exclusive events are events that cannot happen simultaneously.
As you work through Questions 7-9, once again use the process of picking up the cards that are not desired outcomes. This is to show you the greater importance of the probability formula over the ideas of mutually exclusive and not mutually exclusive.
7. What is the probability that Nancy draws a card with the number 1 or the number 2?
8. What is the probability that Nancy draws a card with an odd number or a number divisible by 4? Remember - "divisible by 4" means that 4 will divide evenly into the number. For example, the number 20 is divisible by 4 because 4 divides exactly 5 times into 20.
9. What is the probability that Nancy draws a card with a double-digit number or a
number less than 5?
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Now, suppose that Roger plays a new game in which a person will draw one card from the deck, record the number on it, place it back into the deck, and draw a second card.
10. Why are there 64 total outcomes when drawing two cards as described above? Use
complete sentences for your description.
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PLEASE READ - To help simulate this environment, you will be able to use more than one full deck of cards. To see the possible outcomes, place cards in groups of two, where the card on the left represents the "first draw" and the card on the right represents the "second draw".
11. What is the probability Roger will draw two cards that have double-digit numbers on both of them? To find the number of desired outcomes, create pairings of cards on your desk that would have double-digit numbers on both cards. Remember - the total number of outcomes is 64.
12. What is the probability that Roger draws two cards that have the same number on them?
13. What is the probability that the first card he draws is odd and the second card is even?
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14. In the scenario described above, recall that Roger returns the first card to the deck after being drawn. Because this is done, does the result of the first card influence or "have
anything to do with" the drawing of the second card? If there is an influence, write
"YES". If not, then write "NO".
15. Based on your answer to Question 14, which of the following best classifies the drawing
of two cards from the deck in this manner: independent events or dependent events?
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Learning Task on Probability (Page 2) Name______
Now, as part of a new game, suppose that Michelle will draw a card from the deck, hold onto it, and then draw another card from the deck.
In this process, there are 56 total outcomes.
16. What is the probability that Michelle draws two cards that are both odd?
17. What is the probability that Michelle draws two cards that have a sum of 18?
18. What is the probability that Michelle draws two cards with a sum of exactly 5 or
a sum that is less than 5?
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19. How does the game that Michelle uses here differ from the game that Roger invented?
To answer this question, reference your answer to Questions 14 and/or 15.
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The point of this task - to show you that all probability problems follow the exact same idea: "desired outcomes over total outcomes". While problems involving mutually exclusive events or dependent events may seem more complicated, they all point back to the same basic concept of "desired outcomes over total outcomes".
Answers to Learning Task on Probability Name______
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1 / 1 / 1 / 11 / 2 / 2 / 2
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