#!/usr/bin/env python
# coding: utf-8

# # Chapter 3: Practice Exercises
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# **Exercise 1:** If you flip a fair coin 5 times, what is the probability of
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# A) Getting all heads?
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# B) Getting at least one head?

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# **Exercise 2:** If you roll a pair of fair dice, what is the probability of
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# A) Getting a sum of 1?
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# B) Getting a sum of 5?
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# C) Getting a sum of 12?

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# **Exercise 3:** In a multiple choice quiz there are 5 questions and 3 choices for each question (a,b,c). Jessy did not study for the test at all and she decided to randomly guess the answers. What is the probability that
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# A) the first question she gets right is the 3rd question?
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# B) she get all the questions right?
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# C) she gets at least one question right?

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# **Exercise 4:** In a survey, grade 12 students were asked on their likeability towards quantum computing (QC) & blockchain technology (BT). 70% of the respondents said they like QC, 80% said they like BT while 68% said they like both. Given that a randomly sampled student likes QC, what's the probability that he also likes BT?

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# **Exercise 5:** Researchers collected data on colors of 210 cars in Melbourne. The table below summarizes the results. 
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# |Cars     | Blue | Red   | Black | Total  |
# |---      |---   |---    |---    | ---    |
# |Brand A  | 81   | 23    | 13    | 117    |
# |Brand B  | 19   | 23    | 14    | 56     |
# |Brand C  | 11   | 10    | 16    | 37     |
# |Total    | 111  | 56    | 43    | 210    |
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# A) What is the probability that a randomly chosen car is a Brand A and has the color of Blue?
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# B) What is the probability that a randomly chosen car is a Brand A or has the color of Blue?
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# C) What is the probability that a randomly chosen car is a Blue Brand A car, Red Brand B car or Black Brand C car?
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# D) What is the probability that a randomly chosen Brand A car has the color of Blue?
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# E) What is the probability that a randomly chosen Blue car is a Brand A car?
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# F) What is the probability that a randomly chosen Blue car is not a Brand A?

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# **Exercise 6:** A portfolio's value increases by 18% during a financial boom and by 9% during normal times. It decreases by 12% during a recession. What is the expected return on this portfolio if each scenario is equally likely?

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# **Exercise 7:** Ice cream usually comes in 48  ounces, and ice cream scoops hold about 2 ounces. However, there is some variability in the amount of ice cream in a box as well as the amount of ice cream scooped out. The amount of ice cream in the box is denoted by the random variable X and the amount scooped out as Y. Suppose these random variables have the following means, standard deviations, and variances:
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# |R.V.  | Mean | SD   | Variance |
# |------|------|------|------    |
# |   X  | 48   | 1    | 1        |
# |   Y  | 2    | 0.25 | 0.0625   |
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# A) An entire box of ice cream, plus 3 scoops from a second box is served at a party. How much ice cream do you expect to have been served at this party? What is the standard deviation of the amount of ice cream served?
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# B) How much ice cream would you expect to be left in the box after scooping out one scoop of ice cream? That is, find the expected value of X - Y. What is the standard deviation of the amount left in the box?
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# C) Using the context of this exercise, explain why we add variances when we subtract one random variable from another.

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# *Solutions available [here](https://nbviewer.org/github/imranture/practice_stats/blob/main/ch3-exercises_with_solutions.ipynb).*