use for questions 8 - 11: a bag contains 20 slips of paper, individually numbered 1 - 20. if a slip of paper…

use for questions 8 - 11: a bag contains 20 slips of paper, individually numbered 1 - 20. if a slip of paper and a letter in the word pennsylvania is chosen at random, find each probability. 8. p(less than 15, then a vowel) 9. p(multiple of 4, then v) 10. p(at least 11, then n) 11. p(a prime number, then a consonant) 12. bella guessed on the last three questions on her science test. if each question has five answer choices, what is the probability she got all three correct? 13. it has rained two out of the past nine days. based on this data, what is the probability that it will not rain for the next four days?

use for questions 8 - 11: a bag contains 20 slips of paper, individually numbered 1 - 20. if a slip of paper and a letter in the word pennsylvania is chosen at random, find each probability. 8. p(less than 15, then a vowel) 9. p(multiple of 4, then v) 10. p(at least 11, then n) 11. p(a prime number, then a consonant) 12. bella guessed on the last three questions on her science test. if each question has five answer choices, what is the probability she got all three correct? 13. it has rained two out of the past nine days. based on this data, what is the probability that it will not rain for the next four days?

Answer

Explanation:

Step1: Analyze question 8

The numbers less than 15 out of 1 - 20 are 14 numbers. So the probability of getting a number less than 15 is $\frac{14}{20}$. The word "PENNSYLVANIA" has 12 letters, and 4 vowels. So the probability of getting a vowel is $\frac{4}{12}$. The probability of both events is $\frac{14}{20}\times\frac{4}{12}=\frac{7}{30}\approx 0.233 = 23.3%$.

Step2: Analyze question 9

The multiples of 4 from 1 - 20 are 4, 8, 12, 16, 20, so there are 5. The probability of getting a multiple of 4 is $\frac{5}{20}$. The word "PENNSYLVANIA" has 1 "V", so the probability of getting "V" is $\frac{1}{12}$. The combined - probability is $\frac{5}{20}\times\frac{1}{12}=\frac{1}{48}\approx0.021 = 2.1%$.

Step3: Analyze question 10

The numbers at least 11 from 1 - 20 are 10 numbers. So the probability of getting a number at least 11 is $\frac{10}{20}$. The word "PENNSYLVANIA" has 3 "N"s, so the probability of getting "N" is $\frac{3}{12}$. The combined - probability is $\frac{10}{20}\times\frac{3}{12}=\frac{1}{8}=0.125 = 12.5%$.

Step4: Analyze question 11

The prime numbers from 1 - 20 are 2, 3, 5, 7, 11, 13, 17, 19, so there are 8. The probability of getting a prime number is $\frac{8}{20}$. The word "PENNSYLVANIA" has 8 consonants, so the probability of getting a consonant is $\frac{8}{12}$. The combined - probability is $\frac{8}{20}\times\frac{8}{12}=\frac{8}{30}\approx0.267 = 26.7%$.

Step5: Analyze question 12

Each question has 5 answer - choices. The probability of getting one question correct by guessing is $\frac{1}{5}$. The probability of getting 3 questions correct is $\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}=\frac{1}{125}=0.008 = 0.8%$.

Step6: Analyze question 13

The probability of rain in a day based on the past 9 - day data is $\frac{2}{9}$, so the probability of no - rain in a day is $1-\frac{2}{9}=\frac{7}{9}$. The probability of no - rain for the next 4 days is $(\frac{7}{9})^4=\frac{2401}{6561}\approx0.366 = 36.6%$.

Answer:

  1. $\frac{7}{30}\approx23.3%$
  2. $\frac{1}{48}\approx2.1%$
  3. $\frac{1}{8}=12.5%$
  4. $\frac{8}{30}\approx26.7%$
  5. $\frac{1}{125}=0.8%$
  6. $(\frac{7}{9})^4\approx36.6%$