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

5. Binomial Distribution & Discrete Random Variables

Hypergeometric Distribution

Statistics

5. Binomial Distribution & Discrete Random Variables

Hypergeometric Distribution

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Multiple Choice

Find the probability of drawing a hand of 5 cards from a standard deck that contains exactly 2 hearts.

$0.15$

$0.73$

$0.038$

$0.27$

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Verified step by step guidance

Step 1: Understand the problem. You are tasked with finding the probability of drawing a hand of 5 cards from a standard deck of 52 cards that contains exactly 2 hearts. A standard deck has 13 hearts and 39 non-hearts.

Step 2: Use the combination formula to calculate the number of ways to choose 2 hearts from the 13 available hearts. The formula for combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose.

Step 3: Similarly, calculate the number of ways to choose the remaining 3 cards from the 39 non-hearts using the same combination formula.

Step 4: Multiply the results from Step 2 and Step 3 to find the total number of favorable outcomes (hands with exactly 2 hearts).

Step 5: Divide the total number of favorable outcomes by the total number of possible 5-card hands from the deck, which is calculated as C(52, 5). This gives the probability of drawing a hand with exactly 2 hearts.