Question

#7 20% ofall students are left handed. A class of size 20 meets in a room with 5 left handed and 18 right handed chairs. Find the probability that each student will have a chair to their needs?

Answer 1

Every student will have a place to sit if the number of left handers in a class of 20 are between 2 and 5
Let X be the number of left handers in a class of 20.
Probability that a random student is a left hander = 0.20
P(2 < X < 5) = P(X=2) + P(X=3) + P(X=4) + P(X=5)
P(X=2) = ²⁰C₂(0.20)²(0.80)¹⁸
Simillarly we can evaluate for X=3,4 and 5.
Summing : P(X=2) + P(X=3) + P(X=4) + P(X=5) we will have the final answer.