a) The chance that the roulette wheel will land on a red number is 18/38, or approximately 47.37%.
b) The chance that the roulette wheel will land on a black number is also 18/38, or approximately 47.37%.
c) Since the captain and co-captain are chosen from a box with 12 members, the probability of Steth being chosen as captain is 1/12. After Steth is chosen, there are 11 remaining members, so the probability of Norhen being chosen as co-captain is 1/11. Therefore, the probability that Steth and Norhen are chosen as captain and co-captain, respectively, is (1/12) * (1/11) = 1/132, or approximately 0.0076.
d) In the Christmas raffle with 10,000 entries, if everyone has an equal chance of winning, the probability that Johnny wins the grand prize is 1/10,000, or 0.0001%.
e) Jonalyn has 2 cards with the letter M and a total of 10 cards. The odds of picking a card with the letter M can be expressed as the ratio of the number of cards with the letter M to the total number of cards. Therefore, the odds of randomly picking a card with the letter M are 2/10, or 1/5.
f) The total number of employees in the school is 21 + 39 = 60. The probability that the first person selected is male is the ratio of the number of male employees to the total number of employees, which is 21/60, or 7/20.
g) The probability that the first person selected is female is the ratio of the number of female employees to the total number of employees, which is 39/60, or 13/20.
h) The probability that the first person selected is a teacher is the ratio of the number of teachers to the total number of employees, which is (16 + 24)/60, or 40/60, which simplifies to 2/3.
i) The probability that the first person selected is a non-teaching personnel is the ratio of the number of non-teaching personnel to the total number of employees, which is (5 + 15)/60, or 20/60, which simplifies to 1/3.
j) If all the committee members are teachers, there are 24 teachers to choose from a total of 40 employees (16 + 24). Therefore, the probability that all the committee members are teachers is the ratio of the number of ways to choose 16 teachers from a pool of 40 employees to the total number of ways to choose any combination of employees from the pool of 40. This can be calculated as (C(16, 24) / C(16, 40)), where C(n, r) represents the number of ways to choose r items from a pool of n items.
Answers & Comments
Answer:
a) The chance that the roulette wheel will land on a red number is 18/38, or approximately 47.37%.
b) The chance that the roulette wheel will land on a black number is also 18/38, or approximately 47.37%.
c) Since the captain and co-captain are chosen from a box with 12 members, the probability of Steth being chosen as captain is 1/12. After Steth is chosen, there are 11 remaining members, so the probability of Norhen being chosen as co-captain is 1/11. Therefore, the probability that Steth and Norhen are chosen as captain and co-captain, respectively, is (1/12) * (1/11) = 1/132, or approximately 0.0076.
d) In the Christmas raffle with 10,000 entries, if everyone has an equal chance of winning, the probability that Johnny wins the grand prize is 1/10,000, or 0.0001%.
e) Jonalyn has 2 cards with the letter M and a total of 10 cards. The odds of picking a card with the letter M can be expressed as the ratio of the number of cards with the letter M to the total number of cards. Therefore, the odds of randomly picking a card with the letter M are 2/10, or 1/5.
f) The total number of employees in the school is 21 + 39 = 60. The probability that the first person selected is male is the ratio of the number of male employees to the total number of employees, which is 21/60, or 7/20.
g) The probability that the first person selected is female is the ratio of the number of female employees to the total number of employees, which is 39/60, or 13/20.
h) The probability that the first person selected is a teacher is the ratio of the number of teachers to the total number of employees, which is (16 + 24)/60, or 40/60, which simplifies to 2/3.
i) The probability that the first person selected is a non-teaching personnel is the ratio of the number of non-teaching personnel to the total number of employees, which is (5 + 15)/60, or 20/60, which simplifies to 1/3.
j) If all the committee members are teachers, there are 24 teachers to choose from a total of 40 employees (16 + 24). Therefore, the probability that all the committee members are teachers is the ratio of the number of ways to choose 16 teachers from a pool of 40 employees to the total number of ways to choose any combination of employees from the pool of 40. This can be calculated as (C(16, 24) / C(16, 40)), where C(n, r) represents the number of ways to choose r items from a pool of n items.