Uniform and Non-Uniform Probability
A regular deck of playing cards has 26 red cards and 26 black cards. There are 12 face cards in a deck.
Question 1
Which is an example of non-uniform probability?
Responses
A not drawing a red card from the decknot drawing a red card from the deck
B drawing a face card from the deckdrawing a face card from the deck
C drawing a red card from the deckdrawing a red card from the deck
D drawing a back card from the deckdrawing a back card from the deck
Question 2
Which statement BEST describes a uniform probability model?
Responses
A The desired outcome is certain to occur.The desired outcome is certain to occur.
B No desired outcome is possible.No desired outcome is possible.
C One outcome has a greater chance of occurring.One outcome has a greater chance of occurring.
D All outcomes are equally likely to occur.All outcomes are equally likely to occur.
Answers:
1. B - drawing a face card from the deck is an example of non-uniform probability because not all cards have an equal chance of being drawn. There are only 12 face cards out of 52 total, so the probability of drawing a face card is less than the probability of drawing a non-face card.
2. D - A uniform probability model is one in which all possible outcomes have an equal chance of occurring. In other words, the probability of each outcome is the same. This is true for a deck of playing cards, where each card has an equal chance of being drawn.
Which statement BEST describes a uniform probability model?
Responses
A No desired outcome is possible.No desired outcome is possible.
B One outcome has a greater chance of occurring.One outcome has a greater chance of occurring.
C The desired outcome is certain to occur.
D All outcomes are equally likely to occur.
An experiment was conducted where two dice were rolled 50 times. The sum of the faces are recorded in the chart.
What is the experimental probability of rolling an 8?
Responses
A 14%14%
B 12%12%
C 18%18%
D 16%16%
Question 2
What is the theoretical probability of rolling an 8, and how do the experimental and theoretical probabilities compare?
Responses
A The theoretical probability is 11.1%. The experiment rolled more 8's than would be expected theoretically.The theoretical probability is 11.1%. The experiment rolled more 8's than would be expected theoretically.
B The theoretical probability is 19.4%. The experiment rolled less 8's than would be expected theoretically.The theoretical probability is 19.4%. The experiment rolled less 8's than would be expected theoretically.
C The theoretical probability is 13.9%. The experiment rolled more 8's than would be expected theoretically.The theoretical probability is 13.9%. The experiment rolled more 8's than would be expected theoretically.
D The theoretical probability is 16.7%. The experiment rolled less 8's than would be expected theoretically.The theoretical probability is 16.7%. The experiment rolled less 8's than would be expected theoretically.
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Answer:
1. C - The chart shows that the sum of 8 was rolled 9 times out of 50, so the experimental probability of rolling an 8 is 9/50, which simplifies to 18%.
2. C - The theoretical probability of rolling an 8 with two dice is 5/36, or approximately 13.9%. This can be calculated by finding the number of ways to roll an 8 (5) and dividing by the total number of possible outcomes (36). The experimental probability of rolling an 8 was higher than the theoretical probability, suggesting that 8 may have been more likely to occur due to chance or other factors in the experiment.
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Uniform and Non-uniform Probability
Question 1
Which graph represents a uniform probability distribution?
Responses
A graph A, B, and Cgraph A, B, and C
B graph A onlygraph A only
C graph B onlygraph B only
D graph C onlygraph C only
Question 2
Which BEST describes the difference between a uniform and non-uniform probability model?
Responses
A A uniform probability model has outcomes that are known. Whereas, a non-uniform probability model has outcomes that are not known.A uniform probability model has outcomes that are known. Whereas, a non-uniform probability model has outcomes that are not known.
B A non-uniform probability model has outcomes that all have the same chance of occurring. Whereas, a uniform probability model has outcomes that do not all have the same chance of occurring.A non-uniform probability model has outcomes that all have the same chance of occurring. Whereas, a uniform probability model has outcomes that do not all have the same chance of occurring.
C A non- uniform probability model has outcomes that are known. Whereas, a uniform probability model has outcomes that are not known.A non- uniform probability model has outcomes that are known. Whereas, a uniform probability model has outcomes that are not known.
D A uniform probability model has outcomes that all have the same chance of occurring. Whereas, a non-uniform probability model has outcomes that do not all have the same chance of occurring.A uniform probability model has outcomes that all have the same chance of occurring. Whereas, a non-uniform probability model has outcomes that do not all have the same chance of occurring.
Answers:
1. B - A uniform probability distribution has a constant probability for all outcomes, meaning all bars on the graph should be the same height. Only graph A satisfies this criteria.
2. D - A uniform probability model has outcomes that all have an equal chance of occurring, while a non-uniform probability model has outcomes that do not all have an equal chance of occurring. In a non-uniform probability model, some outcomes may be more likely than others.
In a bag there are 4 purple marbles, 3 green marbles, and 10 yellow marbles. If a student draws one marble what is the sample space?
Responses
A { }{ }
B {Purple, Yellow}{Purple, Yellow}
C {Yellow}{Yellow}
D {Purple, Green, Yellow}
Answer:
D - The sample space is the set of all possible outcomes. In this case, the possible outcomes are drawing a purple marble, a green marble, or a yellow marble. Therefore, the sample space is {Purple, Green, Yellow}.
Ruth is making a necklace for a friend. She has 3 different types of clasps, 2 different chains, and 5 different charms. If she only puts one charm on the necklace, how many different necklaces could she make?
Responses
A 2525
B 6060
C 33
D 3030
E 10