Suppose you have two boxes A and B. Box A contains 7 black marbles, 4 white marbles. Box B contains 7 white and 4 black marbles. A random experiment is performed in two sequential trials by first drawing a marble randomly from box A and putting into Box B. In the second trial after the first trial, a marble is drawn randomly from box B. Plzzz Answer the following questions correctly. a. Are the two trials independent or dependent? Give reasons to support your answer? b. Draw a probability tree diagram to show the execution of this random experiment. ? c. What is the probability of drawing a white marble from box B at the end of 2nd trial?
Suppose you have two boxes A and B. Box A contains 7 black marbles, 4 white marbles. Box B contains 7 white and 4 black marbles. A random experiment is performed in two sequential trials by first drawing a marble randomly from box A and putting into Box B. In the second trial after the first trial, a marble is drawn randomly from box B.
Plzzz Answer the following questions correctly.
a. Are the two trials independent or dependent? Give reasons to support your answer?
b. Draw a
c. What is the probability of drawing a white marble from box B at the end of 2nd trial?
d. What is the probability of drawing a black marble from box B at the end of 2nd trial?
e. Identify all the mutually exclusive
f. If we reverse the scenario, then what is the probability of drawing a black marble from box A given that a white marble is drawn from box B.?
Q#02.
HBL Bank Pvt LtD. is studying its ATM use in the Gulshan-e-Iqbal area of Karachi. A sample of 30 ATMs showed they were used in the given number of times (in seconds) on a particular day, as shown in Table 1.
- Identify the presence of outliers in this dataset
- After removing the outliers (if present) from the given dataset, what is the expected or average number of times (in seconds) the ATM is used in the new dataset (if outliers were detected and removed). Show your results with errors in the statistical expected or average value.
|
83.24 |
64.01 |
84.23 |
76.20 |
84.21 |
54.29 |
5.11 |
59.21 |
70.23 |
61.01 |
|
63.10 |
80.23 |
84.21 |
73.20 |
68.11 |
52.19 |
65.22 |
90.16 |
52.16 |
177.21 |
|
95.23 |
36.15 |
48.12 |
16.18 |
59.32 |
84.22 |
195.13 |
47.18 |
87.13 |
26.11 |
Q#03.
Suppose in a class there are 170 students. Of those 170 students, 90 are males and 80 are females. Among 90 male students, 55 like playing the game of football and 35 do not like it. Among 80 female students, 10 like playing the game of football and 70 do not like it.
- Represent all this information in the form of a cross tabulation or probability
contingency table . - Show probability tree diagrams for all the possible random events that can occur (with their probabilities) if a student is picked randomly in this class.
Q#04
- Formulate a dataset using the frequency distribution table of the random experiment for the number of boys in a committee of 3 people selected at random from 4 boys and 3 girls. Random variable or dataset indicates the number of boys.
- What is the expected or average number of boys that can be selected in part a)? Verify this answer using a frequency histogram.
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