Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 76% of the time because it costs less, and he takes a taxi the other 24% of the time. When taking the subway, he arrives at work on time 74% of the time, whereas he makes it on time 95% of the time when traveling by taxi. (Give your answers correct to three decimal places.)
(a) What is the probability that Juan took the subway and is at work on time on any given day?

Question

Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 76% of the time because it costs less, and he takes a taxi the other 24% of the time. When taking the subway, he arrives at work on time 74% of the time, whereas he makes it on time 95% of the time when traveling by taxi. (Give your answers correct to three decimal places.) 
(a) What is the probability that Juan took the subway and is at work on time on any given day?

anonymous · Answer

multiply the probabilities together. 
$$.76\times .74$$

anonymous · Answer

these are independent events so probabilities are multiplied

anonymous · Answer

actually they are not independent

anonymous · Answer

i did that and it tells me it is wrong. i multiplied .76*.74 = 0.56

anonymous · Answer

but 0.74 is the probability he is on time GIVEN he took the subway, and that is why you multiply 
$$P(A\cap B) = P(B)\times P(A|B)$$

anonymous · Answer

$$0.5624$$ you need 3 decimal place accuracy, so put 0.562

anonymous · Answer

yeah - thats right

anonymous · Answer

OK!! thats what i missed was the third decimal.. thanks guys