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in the only deluxe room

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by sanju09 » Wed Jul 11, 2012 2:46 am
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?
A. 1/8
B. 2/9
C. 2/7
D. 3/8
E. ½


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by niketdoshi123 » Wed Jul 11, 2012 3:41 am
sanju09 wrote: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?
A. 1/8
B. 2/9
C. 2/7
D. 3/8
E. ½


Source: collegeboard.org
Total seniors = 100
Each senior's name in the lottery = 3 times
Total seniors' name in the lottery (Se) = 300
Similarly,
Total juniors' name in the lottery (J)= 150*2 = 300
and total sophomores' name in the lottery (So)= 200

P(Se) = Se/(Se+J+So) = 300/(300+300+200) = 3/8.
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by karthikpandian19 » Wed Jul 11, 2012 8:47 pm
No of times - Senior = 100*3 times = 300
No of times - Junior = 150*2 times = 300
No of times - Sophomore = 200*1 times= 200

Total - 300 + 300 + 200 = 800 is the total times

probability of chance of a senior = Senior times / total = 300/800 = 3/8

Answer: 3/8 (D)
sanju09 wrote: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?
A. 1/8
B. 2/9
C. 2/7
D. 3/8
E. ½


Source: collegeboard.org
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