megan has a virtual bookshelf with 5 fantasy books, 8 memoirs, 12 history books, and 17 novels. she has the…
megan has a virtual bookshelf with 5 fantasy books, 8 memoirs, 12 history books, and 17 novels. she has the virtual bookshelf shuffle the books with replacement 20 times and records the results.\n\ngenre frequency\nfantasy 1\nmemoir 5\nhistory 5\nnovel 9\n\nfill in the blanks to complete the sentences comparing the experimental and theoretical probabilities.\n\nthe theoretical probability of selecting a fantasy book is \nthan the experimental probability.\n\nthe theoretical probability of selecting a memoir is \nthan the experimental probability.\n\nthe theoretical probability of selecting a history book is \nthan the experimental probability.\n\nthe theoretical probability of selecting a novel is \nthan the experimental probability.
Answer
Explanation:
Step1: Calculate total number of books
$5 + 8+12 + 17=42$
Step2: Calculate theoretical probabilities
- Probability of fantasy book: $P_{f}=\frac{5}{42}\approx0.119$
- Probability of memoir: $P_{m}=\frac{8}{42}=\frac{4}{21}\approx0.190$
- Probability of history book: $P_{h}=\frac{12}{42}=\frac{2}{7}\approx0.286$
- Probability of novel: $P_{n}=\frac{17}{42}\approx0.405$
Step3: Calculate experimental probabilities
- Probability of fantasy book: $P_{f - exp}=\frac{1}{20}=0.05$
- Probability of memoir: $P_{m - exp}=\frac{5}{20}=0.25$
- Probability of history book: $P_{h - exp}=\frac{5}{20}=0.25$
- Probability of novel: $P_{n - exp}=\frac{9}{20}=0.45$
Step4: Compare probabilities
- For fantasy: $\frac{5}{42}\approx0.119>0.05$, so theoretical > experimental.
- For memoir: $\frac{4}{21}\approx0.190<0.25$, so theoretical < experimental.
- For history: $\frac{2}{7}\approx0.286<0.25$, so theoretical < experimental.
- For novel: $\frac{17}{42}\approx0.405<0.45$, so theoretical < experimental.
Answer:
The theoretical probability of selecting a fantasy book is greater than the experimental probability. The theoretical probability of selecting a memoir is less than the experimental probability. The theoretical probability of selecting a history book is less than the experimental probability. The theoretical probability of selecting a novel is less than the experimental probability.