Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

4. Probability

Addition Rule

Statistics

4. Probability

Addition Rule

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2:16 minutes

Problem 3.3.17c

Textbook Question

17. Selecting a Card A card is selected at random from a standard deck of 52 playing cards. Find the probability of each event.
c. Randomly selecting a 9 or a face card

Verified step by step guidance

Step 1: Understand the problem. A standard deck of 52 playing cards consists of 4 suits (hearts, diamonds, clubs, spades), each containing 13 cards. The goal is to calculate the probability of randomly selecting either a 9 or a face card (Jack, Queen, King).

Step 2: Determine the total number of favorable outcomes. There are 4 nines in the deck (one for each suit) and 12 face cards (Jack, Queen, King, each appearing in all 4 suits). Add these together to find the total number of favorable outcomes: 4 (nines) + 12 (face cards) = 16.

Step 3: Recall the formula for probability. The probability of an event is given by the formula:

\frac{favorable outcomes}{total outcomes}

. In this case, the total number of outcomes is the total number of cards in the deck, which is 52.

Step 4: Substitute the values into the formula. Use the favorable outcomes (16) and total outcomes (52) to calculate the probability:

\frac{16}{52}

Step 5: Simplify the fraction if necessary. To express the probability in its simplest form, divide the numerator and denominator by their greatest common divisor (GCD). This step ensures the fraction is reduced to its lowest terms.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In the context of selecting a card from a deck, it quantifies how many favorable outcomes exist compared to the total number of possible outcomes. For example, if there are 4 nines and 12 face cards in a deck, the probability of selecting either is calculated by dividing the number of favorable outcomes by the total number of cards.

Favorable Outcomes

Favorable outcomes refer to the specific results that satisfy the conditions of the event being analyzed. In this case, the favorable outcomes for selecting a 9 or a face card include the 4 nines and the 12 face cards (Jack, Queen, King). Understanding how to identify and count these outcomes is crucial for calculating the overall probability of the event.

Total Outcomes

Total outcomes represent the complete set of possible results in a probability scenario. For a standard deck of 52 playing cards, the total outcomes are simply the total number of cards in the deck. This concept is essential for determining the probability, as it serves as the denominator in the probability formula, allowing for the comparison of favorable outcomes to the overall possibilities.

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Textbook Question

Graphical Analysis In Exercises 7 and 8, determine whether the events shown in the Venn diagram are mutually exclusive. Explain your reasoning.

Textbook Question

Recognizing Mutually Exclusive Events In Exercises 9–12, determine whether the events are mutually exclusive. Explain your reasoning.

10. Event A: Randomly select a student with a birthday in April.

Event B: Randomly select a student with a birthday in May.

Textbook Question

13. Students A physics class has 40 students. Of these, 12 students are physics majors and 16 students are minoring in math. Of the physics majors, three are minoring in math. Find the probability that a randomly selected student is minoring in math or a physics major.

Textbook Question

16. Can Defects Of the cans produced by a company, 96% do not have a puncture, 93% do not have a smashed edge, and 89.3% have neither a puncture nor a smashed edge. Find

the probability that a randomly selected can does not have a puncture or a smashed edge.

Textbook Question

18. Rolling a Die You roll a die. Find the probability of each event.

b. Rolling a 2 or an odd number

Textbook Question

Mental Health A survey asks 4805 parents the severity of the mental issues they experienced from the coronavirus pandemic. The results are shown in the table. A parent is randomly selected from the sample. Find the probability of each event. (Adapted from Kaiser Family Foundation)

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c. The parent did not have major mental health issues or is a mother.

Textbook Question

25. Working from Home The table shows the results of a survey that asked 1811 people how often they work from home. A person is selected at random from the sample. Find the probability of each event.

b. The person is female or does not work from home.

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Textbook Question

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.

a. The person wears only contacts or only glasses.

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17. Selecting a Card A card is selected at random from a standard deck of 52 playing cards. Find the probability of each event.c. Randomly selecting a 9 or a face card

Key Concepts

Probability

Favorable Outcomes

Total Outcomes

Watch next

17. Selecting a Card A card is selected at random from a standard deck of 52 playing cards. Find the probability of each event.
c. Randomly selecting a 9 or a face card