1.

In a certain college, 4% of ·boys and 1 % of girls are taller than 1.75 metres. Furthermore, 60% of the students are girls. If a student is selected at random and is taller than 1.75 metres, what is the probability that the selected student is a girl?

Answer»


SOLUTION :LET `E_1and E_2` be the EVENTS of selecting a boy and a girl respectively.
Then, `P(E_1)=40/100=2/5,and P(E_2)=60/100=3/5`.
Let E = EVENT that the student selected is taller than 1.75 m.
Then `P(E//E_1)=4/100=1/25and P(E//E_2)=1/100`.
Probability that the selected student is a girl, givne that she is taller than 1.75 m
`=P(E_2//E)`
`=(P(E//E_2).P(E_2))/(P(E//E_1).P(E_1)+P(E//E_2.P(E_2))`


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