Question

Juana, who has just received a postgraduate degree, feels lucky to have found a permanent job in this tough economy. She faced these statistics: Only 2/3 of the graduates of "top flight" schools and 1/3 of the graduates of lower ranked schools found permanent jobs within nine months of graduation. The top flight schools comprise 1/4 of the total number. What is the probability that Juana attended a top flight school?

Answer 1

P( top school ) = 0.25
P( lower ranked school ) = 0.75

P( permanent job | top school ) = (2/3)
P( permanent job | lower ranked school ) = (1/3)

Therefore using law of total probability, we get:

P( permanent job ) = P( permanent job | top school ) P( top school ) + P( permanent job | lower ranked school )P( lower ranked school )

P( permanent job ) = (2/3)*0.25 + (1/3)*0.75 = 0.4167

Using Bayes theorem now, we get:

P( top school | permanent job ) = P( permanent job | top school ) P( top school ) / P( permanent job )

P( top school | permanent job ) = (2/3)*0.25 / 0.4167

P( top school | permanent job ) = 0.4

Therefore 0.4 is the required probability here.