A survey is taken by 200 people. 90 people like red and 110 people dislike red. If you randomly choose a person what is the chance they will like red? Fraction simplest form.

Question

Word CLEAN is put on paper and put in a hat. What is probability you will choose a vowel? Answer as percent
You flipped a count 20 times and got a tail 13 of those times. What is the experimental probability of getting a heads? (ratio simplest form)
Flipped 3 pennies and did this 100 times. You got 3 tails 40 times. What is the difference between the experimental probability of getting 3 tails and the theoretical probability? (simplified fraction)
A single coin is tossed 500 times. Tails was observed 200 times. What is the long-run relative frequency of Heads? Decimal form

Answer 1

Let's solve each question step by step.

1. Chance of liking red:

   • Total people surveyed = 200
   • People who like red = 90
   • Probability of randomly choosing someone who likes red = \(\frac{\text{Number of people who like red}}{\text{Total number of people}} = \frac{90}{200} = \frac{9}{20}\)
   • Simplest form is \(\frac{9}{20}\).

2. Probability of choosing a vowel from the word "CLEAN":

   • The word "CLEAN" has the letters: C, L, E, A, N
   • Number of vowels (E, A) = 2
   • Total letters in "CLEAN" = 5
   • Probability of choosing a vowel = \(\frac{2}{5}\)
   • To express this as a percentage: \(\frac{2}{5} \times 100 = 40%\)
   • The answer is 40%.

3. Experimental probability of getting heads after flipping a coin 20 times:

   • Total flips = 20
   • Tails = 13; thus, Heads = 20 - 13 = 7
   • Experimental probability of getting heads = \(\frac{\text{Number of heads}}{\text{Total flips}} = \frac{7}{20}\)
   • Simplest form is \(\frac{7}{20}\).

4. Difference between the experimental probability of getting 3 tails and the theoretical probability:

   • Experimental probability of getting 3 tails: In 100 sets, 3 tails occurred 40 times, thus: \[ \text{Experimental probability} = \frac{40}{100} = \frac{2}{5} \]
   • Theoretical probability of getting 3 tails when flipping 3 pennies (each penny has a 50% chance to be tails): \[ P(\text{3 tails}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]
   • To find the difference: \[ \text{Difference} = \frac{2}{5} - \frac{1}{8} \]
   • Converting \(\frac{2}{5}\) to 40/80 for a common denominator with 8: \[ \frac{2}{5} = \frac{32}{80} \]
   • Therefore: \[ \text{Difference} = \frac{32}{80} - \frac{10}{80} = \frac{22}{80} = \frac{11}{40} \]
   • The difference is \(\frac{11}{40}\).

5. Long-run relative frequency of Heads:

   • Total flips = 500
   • Tails observed = 200; thus, Heads = 500 - 200 = 300
   • Long-run relative frequency of Heads = \(\frac{300}{500} = \frac{3}{5}\)
   • In decimal form: \(\frac{3}{5} = 0.6\)
   • The answer is 0.6.

Here’s a summary of all answers:

1. \(\frac{9}{20}\)
2. 40%
3. \(\frac{7}{20}\)
4. \(\frac{11}{40}\)
5. 0.6