Probabilities - Statistics - Exercise, Exercises of Statistics

These are the notes of Exercise of Statistics. Key important points are: Probabilities, Theoretical Probability, Formula, Lowest Terms, Outcomes, Dealt, Rolled Twice

Typology: Exercises

2012/2013

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Lesson
Probabilities
Use the theoretical probabilit
y
formula to solve the problem. Express the probabilit
y
as a fraction
reduced to lowest terms.
1) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of
getting a 7.
2) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of
getting a 6.
3) You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture
card.
4) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1,
5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4,
2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6,
5), (6, 6),}. Find the probability of getting two numbers whose sum is less than 13.
5) Use the spinner below to answer the question. Assume that it is equally probable that the pointer
will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again.
Find the probability that the arrow will land on 3 or 4.
Prestatistics
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Lesson

Probabilities

Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms.

  1. (^) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 7.

  2. A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 6.

  3. (^) You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.

  4. (^) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is less than 13.

  5. Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that the arrow will land on 3 or 4.

Prestatistics

Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probability as a decimal, rounded to the nearest thousandth, if necessary.

  1. (^) The table below represents a random sample of the number of deaths per 100 cases for a certain illness over time. If a person infected with this illness is randomly selected from all infected people, find the probability that the person lives 3-4 years after diagnosis. Years after Diagnosis Number deaths 1-2 15 3-4 35 5-6 16 7-8 9 9-10 6 11-12 4 13-14 2 15+ 13

The chart below shows the percentage of people in a questionnaire who bought or leased the listed car models and were very satisfied with the experience.

Model A 81% Model B 79% Model C 73% Model D 61% Model E 59% Model F 57%

  1. The empirical probability that a person with a model shown is very satisfied with the experience is 73 100

. What is the model?

Solve the problem.

  1. (^) Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They arrive randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive first and Keith will arrive last.

  2. (^) Six students, A, B, C, D, E, F, are to give speeches to the class. The order of speaking is determined by random selection. Find the probability that (a) E will speak first (b) that C will speak fifth and B will speak last (c) that the students will speak in the following order: DECABF (d) that A or B will speak first.

Prestatistics

Answer Key Testname: 31_PROBABILITIES

  1. 0 2)^16

  2. 133

  3. 1 5)^25

  4. 100 35 ; 0.

  5. C

  6. 720; 24; 301

9)^16 ; 24 1 ; 720 1 ; (^13)

  1. 165; 20; 334

  2. 5985 1 ; 17168

  3. 338

Prestatistics