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.
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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