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Probability Questions

1. A school in Bangkok requires that students take an entrance examination. After the examination, there is a drawing where 5 students are randomly selected from
each group of 40 for automatic acceptance into the school, regardless of their performance on the examination. The drawing consists of placing 35 red and 5 green pieces of paper into a box. Each student picks a piece of paper from the box and then does not return the piece of paper to the box. The 5 lucky students who pick the green pieces are automatically accepted into the school.

a. What is the probability that the first person wins automatic

b. What is the probability that the last person wins automatic

c. If the students are chosen by the order of their seating,
does this give the student who goes first a better chance
of winning than the second, third, . . . person? (Hint:
Imagine that the 40 pieces of paper have been mixed up
and laid in a row so that the first student picks the first
piece of paper, the second student picks the second piece
of paper, and so on.)

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Solution Preview

The probability that any one student will win acceptance is 5/40, or 1/8.

Look at part c first. If all the pieces of paper were mixed ...