Question

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.

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)