Question

A school tracked Students' French proficiency and whether not they had a speaking partner outside of...

A school tracked Students' French proficiency and whether not they had a speaking partner outside of school. The results are given in the following table.

Basic Intermediate Advanced Total
Speaking partner 10 30 20 60
No Speaking partner 115 45 80 240
Total 125 75 100 300

What is the probability that a student achieved Intermediate proficiency or had a Speaking Partner?

And state that these statement is true or false and the reason why do you think that

The events "Advanced" and "Speaking Partner" are independent events.


Homework Answers

Answer #1

Ans:

Probability that a student achieved Intermediate proficiency or had a Speaking Partner

=P(Intermediate)+P(Speaking Partner)-P(Intermediate proficiency and Speaking Partner)

=(75/300)+(60/300)-(30/300)

=(75+60-30)/300

=105/300

=0.35

For two events A and B to be independent,P(A and B)=P(A)*P(B)

P(Advanced and Speaking partner)=20/300=1/15

P(Advanced)=100/300=1/3

P(Speaking partner)=60/300=1/5

P(Advanced)*P(Speaking Partner)=(1/3)*(1/5)=1/15

As,both probabilities are equal,so two events are independent.

(True)

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