P( passing english)= 0.70, P( passing spanish)= 0.6, P(passing both)=0.45. What is the probability he will pass spanish if its known he will pass english?

Question

Deals with Statistics and Probability

Answer 1

The most intuitive way to solve this is to draw a Venn diagram

[ P(pass English) = .70 ]

{ P(pass Spanish) = .60 }

P(pass English and Spanish) = .45

[ .25 pass English only .45 pass English and Spanish ]

{ P(pass English and Spanish) = .45 P(pass Spanish only) = .15) }

We are looking for probability of passing Spanish knowing student has passed English.

Here we are in the universe of passing English. In this universe some pass English and Spanish.

So the probability we are interested in is .45 / .70 = .643

Another method for solving this comes from using the formula for conditional probability.

We are looking for P(S | E) = P(S intersect E)

----------------------

P(E)

This gives .45 / .70 which is .643