Question

N general 20% of all 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

All students will have a chair to their needs. So a 100% probability.

Answer 2

The probability that each student will have a chair to their needs is P=0.6698.

Explanation:

If 20 % of all students are left handed (LHS) and the class size is 20, there will be 4 left handed students and 16 right handed or ambidextrous (RHS). Then there are 5 left handed chairs (LHC) and 18 right handed (RHC), so there are 23 chairs. Now, you have to estimate the proportion for LHS, RHS, LHC and RHC.

P(LHS) = 4/20 ⇒ 0.2.

P(RHS) = 16/20 = 0.8.

P(LHC) = 5/23 = 0.217.

P(RHC) = 18/23 = 0.783.

Then to find the probability that each student will have a chair to their needs, we have to multiply P(LHS)xP(LHC) and P(RHS)xP(RHC) and sum.

⇒P(LHS)xP(LHC) + P(RHS)xP(RHC) = (0.2 x 0.217) + (0.8 x 0.783)

⇒ P(LHS)xP(LHC) + P(RHS)xP(RHC) = 0.6698.

Summarizing, the probability that each student will have a chair to their needs, is 0.6698.