Question
The letters from the word FOOTBALL are written on 8 cards with one letter on each card. One card will be drawn randomly and then placed back into the stack. If this experiment is repeated 840 times, about how many times should you expect to draw a consonant?
Ask by Pritchard Mccoy.
Jan 29,2025 00:05
UpStudy AI Solution
Tutor-Verified Answer
Answer
You should expect to draw a consonant 525 times out of 840 trials.
Solution
To determine the expected number of times a consonant is drawn in 840 trials, follow these steps:
1. **Identify the Letters in "FOOTBALL":**
- The word "FOOTBALL" consists of the letters: F, O, O, T, B, A, L, L.
- Total letters: **8**.
2. **Classify Letters as Vowels or Consonants:**
- **Vowels:** A, O, O.
- **Consonants:** F, T, B, L, L.
- Number of vowels: **3**.
- Number of consonants: **5**.
3. **Calculate the Probability of Drawing a Consonant:**
- Probability \( P \) of drawing a consonant is the number of consonants divided by the total number of letters:
\[
P = \frac{5}{8}
\]
4. **Determine the Expected Number of Consonant Draws in 840 Trials:**
- Multiply the probability by the total number of trials:
\[
\text{Expected draws} = \frac{5}{8} \times 840 = 525
\]
**Conclusion:**
You should expect to draw a consonant **525 times** out of 840 trials.
**Answer:** 525
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
In the word "FOOTBALL," the letters consist of 3 vowels (O, O, A) and 5 consonants (F, T, B, L, L). The probability of drawing a consonant is calculated as the number of consonants divided by the total number of letters: 5 consonants / 8 total letters = 5/8. If the experiment is repeated 840 times, you would expect to draw a consonant approximately (5/8) * 840, which equals 525 times.
If you want to visualize it, picture a bowl filled with 8 colorful cards: 5 sturdy consonant cards standing proudly among 3 vowel buddies. So, every time you reach into that bowl, your chances of pulling out a consonant are a hearty 5 out of 8—like having 5 delicious candies waiting for you!
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