A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?
100*3= 300 Senior tickets
150*2=300 Junior Tickets
300*1=200 Sophomore Tickets
800 Total
300/800 chance
3 out of 8.
To find the probability that a senior's name will be chosen, we need to calculate the total number of entries for seniors and divide it by the total number of entries for all students.
The number of entries for seniors can be found by multiplying the number of seniors by the number of times their names are placed in the lottery: 100 seniors * 3 entries per senior = 300 entries for seniors.
The total number of entries for all students can be found by adding the total number of entries for each grade level: 300 entries for seniors + 150 juniors * 2 entries per junior + 200 sophomores * 1 entry per sophomore = 300 + 300 + 200 = 800 total entries.
Therefore, the probability that a senior's name will be chosen is: 300 senior entries / 800 total entries = 0.375 or 37.5%.
To find the probability that a senior's name will be chosen, we need to determine the total number of entries in the lottery and the number of entries that belong to seniors.
First, let's calculate the total number of entries in the lottery. Each senior has their name entered three times, each junior has their name entered twice, and each sophomore has their name entered once.
Total number of entries = (number of seniors * 3) + (number of juniors * 2) + (number of sophomores * 1)
= (100 * 3) + (150 * 2) + (200 * 1)
= 300 + 300 + 200
= 800
So, there are a total of 800 entries in the lottery.
Next, to find the number of entries that belong to seniors, we multiply the number of seniors by the number of times their name is entered.
Number of entries for seniors = number of seniors * number of times each senior's name is entered
= 100 * 3
= 300
Therefore, there are 300 entries in the lottery that belong to seniors.
Finally, we can now calculate the probability that a senior's name will be chosen by dividing the number of entries that belong to seniors by the total number of entries in the lottery.
Probability that a senior's name will be chosen = Number of entries for seniors / Total number of entries
= 300 / 800
= 3/8
Hence, the probability that a senior's name will be chosen is 3/8.