A ___________ Is A Value Between Zero And One, Inclusive ✓ Solved

A ___________ is a value between zero and one, inclusive,

Fill in the space. (2 points each) A ___________ is a value between zero and one, inclusive, describing the relative chance or likelihood an event will occur. An experiment with more than one step is called _______________ ________________. An _________ is a subset of outcomes from the sample space. Using the _____________ viewpoint, an individual makes an educated guess and then estimates or assigns the probability. Using the ________________ viewpoint, the probability of an event happening is computed by dividing the number of favorable outcomes by the total number of trials.

If several events are described as ______________ ________________, then the occurrence of one event has no common outcome with the other events. The ____________ _________ is used to determine the probability of an event occurring by subtracting the probability of the event not occurring from 1. The special rule of multiplication requires that two events and are _______________. A probability that measures the likelihood that an event occurs given that another event occurs is called ________________ __________________. _________________ is the selection of objects from a group without regard to their arrangement.

Free Response Question (You must show all your work to earn full credit) Fred exercises regularly. His fitness log for the last 12 months shows that he jogged 30% of the days, rode his bike 20% of the days, and did both on 12% of the days. (5 points) What is the probability that Fred would either jog or ride his bike on any given day? What is the probability that Fred would neither jog nor ride his bike on any given day? In how many ways can you arrange the letters in the word GRAMMATICAL ? (10 points) Solve the following (Show your work): (5 points each) (b) (c) Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly. What is the probability they are both juniors or both seniors? (Use Multiplication Rule for Dependent Events) (10 points) Consider a jar containing 4 blue marbles, 9 green marbles, and 5 yellow marbles. Suppose each marble has an equal chance of being picked from the jar. Find: (5 points each) Probability of selecting a yellow marble. Probability of selecting a blue marble. (c) Probability of selecting a green marble. The student council at one high school must choose two representatives from each of the sophomore, junior, and senior classes to attend the annual student council convention. If there are 6 sophomores, 5 juniors, and 7 seniors on the student council, in how many ways can the group be chosen for the convention?

Paper For Above Instructions

Statistics is a crucial field of study that allows us to understand and analyze data effectively. In statistical terminology, a probability is a value between zero and one inclusive, describing the relative chance or likelihood that an event will occur (Triola, 2018). An experiment with more than one step is termed a multistage experiment. Within statistics, an event is a subset of outcomes from the sample space. When we use the subjective viewpoint of probability, we make educated guesses based on personal judgment and experiences. In contrast, the classical viewpoint involves calculating the probability based on the ratio of favorable outcomes to the total number of trials (Scheaffer, 2017).

In instances where events are described as mutually exclusive, the occurrence of one event precludes the possibility of the other events occurring simultaneously. To compute the probability of an event occurring, we can use the complement rule, which states that we can determine the probability of an event by subtracting the probability of the event not occurring from one (Bluman, 2018). Additionally, the special rule of multiplication is applicable when two events are independent. A conditional probability measures the likelihood that an event occurs given that another event has already occurred (Mendenhall, Beaver, & Beaver, 2019). Furthermore, combinations refer to the selection of objects from a group where the order of selection does not matter.

Now, let's analyze the fitness log of Fred over the last twelve months. Fred jogged for 30% of the days, rode his bike for 20% of the days, and engaged in both activities for 12% of the days. To find the probability that Fred would either jog or ride his bike on any given day, we can use the principle of inclusion-exclusion:

P(Jog or Ride) = P(Jog) + P(Ride) - P(Jog and Ride)P(Jog or Ride) = 0.30 + 0.20 - 0.12 = 0.38.

This means that the probability that Fred would either jog or ride his bike on any given day is 0.38 or 38%.

To find the probability that Fred would neither jog nor ride his bike on a given day, we can compute it using the complement rule:

P(Neither Jog nor Ride) = 1 - P(Jog or Ride)P(Neither Jog nor Ride) = 1 - 0.38 = 0.62.

Hence, the probability that Fred would neither jog nor ride his bike on any given day is 0.62 or 62%.

Next, we will look at the arrangements of the letters in the word GRAMMATICAL. To determine the total number of arrangements, we note that the word consists of 11 letters where 'A' appears twice, 'G', 'R', 'M', 'T', 'I', 'C', and 'L' appear once. The formula for permutations of letters in a word is calculated by:

n! / (n1! n2! ... * nk!),

where n is the total number of letters, and n1, n2, …, nk are the frequencies of the repeated letters:

Thus, the total arrangements of GRAMMATICAL = 11! / (2!) = 1995840.

Next, we consider the scenario where five juniors and four seniors apply for two open student council positions. To find the probability that both selected members are juniors or both are seniors, we first calculate the probabilities for both scenarios and then combine them.

For both being juniors:

P(Both Juniors) = (5/9) * (4/8) = 20/72.

For both being seniors:

P(Both Seniors) = (4/9) * (3/8) = 12/72.

So, the total probability that they are both juniors or seniors is:

P(Both Juniors or Both Seniors) = P(Both Juniors) + P(Both Seniors) = 20/72 + 12/72 = 32/72 = 4/9.

Now, regarding the jar containing 4 blue marbles, 9 green marbles, and 5 yellow marbles:

The total number of marbles is 4 + 9 + 5 = 18.

The probability of selecting a yellow marble is:

P(Yellow) = 5/18.

The probability of selecting a blue marble is:

P(Blue) = 4/18 = 2/9.

The probability of selecting a green marble is:

P(Green) = 9/18 = 1/2.

Finally, the student council must choose two representatives from the sophomore, junior, and senior classes. If there are 6 sophomores, 5 juniors, and 7 seniors, the number of ways to choose representatives can be calculated as follows:

Ways to choose sophomores = C(6, 2) = 15.Ways to choose juniors = C(5, 2) = 10.Ways to choose seniors = C(7, 2) = 21.

Thus, the total number of ways to select representatives is:

Total Ways = 15 10 21 = 3150.

References

  • Bluman, A. G. (2018). Elementary Statistics: A Step By Step Approach. McGraw-Hill Education.
  • Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2019). Introduction to Probability and Statistics. Cengage Learning.
  • Triola, M. F. (2018). Elementary Statistics. Pearson.
  • Weiss, N. A. (2016). . Pearson.
  • Moore, D. S., Notz, W. I., & Fligner, M. A. (2017). Statistics. McGraw-Hill Education.
  • Siegel, A. F., & Castellan, N. J. (2018). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill Education.
  • Casella, G., & Berger, R. L. (2016). Statistical Inference. Cengage Learning.
  • Devore, J. L. (2018). Probability and Statistics. Cengage Learning.
  • Hogg, R. V., & Tanis, E. A. (2015). Probability and Statistical Inference. Pearson.
  • Gravetter, F. J., & Wallnau, L. B. (2017). Statistics. Cengage Learning.

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