Use the two-way table of data from another student survey to answer the following question. Like Aerobic Exercise Like Weight Lifting Yes No Total Yes

1. The Office of Prefect of Students conducted a survey to students to determine their preferred mode of learning. Out of 600 students, 365 favored synchronous online learning, 158 favored asynchronous, while the rest favored modular instruction. What is the probability that a randomly selected student favored:

1. asynchronous mode of learning
2. modular or asynchronous mode of learning?
3. synchronous or modular mode of learning?
4. neither synchronous nor asynchronous mode of learning?

 

A coin is tossed and a die is rolled, what is the probability of getting head in tossing a coin and getting an odd number when casting a fair die?

 

      3. A vase contains 8 pink, 9 purple, and 11 yellow tulips. You randomly choose a flower from the vase to take home. Your best friend randomly chooses another flower from the vase to take home. What is the probability that you choose pink tulips and your best friend chooses purple tulips?

 

      4. Ace is planning to enroll in short courses in TESDA. He plans to take Bread and Pastry Production, and Food and Beverage Service. The probability of finishing Bread and Pastry Production is 48%, and 53% for Food and Beverage Service. If the probability of finishing both courses is 40%, what is the probability of passing at least one course?

 

      5. According to DOST-FNRI, 24.7% of the population of Filipino elderly, 60 years old and above, are obese. If we select three elderly at random, what is the probability that all selected will be obese?

 

Complete the table.
GradeFrequencyRelative frequency
A5
B11
C16
D5
F1
(Round to two decimal places as needed.)

Find a real-life data set that can be represented by a two-way table. Then make a two-way table for the data set.

The following is a two-way table showing preferences for an award (A, B, C) by gender for the students sampled in survey. Test whether the data indicate there is some association between gender and preferred award.
$\begin{array}{|ccccc|}\hline & \text{A}& \text{B}& \text{C}& \text{Total}\\ \text{Female}& 20& 76& 73& 169\\ \text{Male}& 11& 73& 109& 193\\ \text{Total}& 31& 149& 182& 360\\ \hline\end{array}$
Chi-square statistic=?
p-value=?
Conclusion: (reject or do not reject $H_0$)
Does the test indicate an association between gender and preferred award? (yes/no)

Please, answer the question: if there is no association between the categorical variables, which of the following is true?
a) The observed counts in the two-way table should be close to the expected points.
b) The observed counts in the two-way table will be different from the expected points.
c) The chi-square statistic will have a large value and the observed counts in a two-way table will be very different from the expected points.
d) The chi-square statistic will have a large value.

The following two-way table displays information about favorite sports cars that resulted from a survey given to all students at Shore High School.

$\begin{array}{|ccccc|}\hline & \text{Corvette (C)}& \text{Porsche (P)}& \text{Ferrari (F)}& \text{Total}\\ \text{Boys (B)}& 90& 60& 120& 270\\ \text{Girls (G)}& 110& 141& 79& 330\\ \text{Total}& 200& 201& 199& 600\\ \hline\end{array}$

What is the probability that a randomly selected student from this school is a boy?

Use the table below and answer the questions.
1) P (> 1 car | 2 to 4 kids) = ?
2) P (< 4 kids or ${\displaystyle \le }$ 2 cars) = ?