Lazar drives to work every day and passes two independently operated traffic lights. The probability that both lights are green is 0.41. The probability that the first light is green is 0.59. What is the probability that the second light is green, given that the first light is green?

0.71

0.69

0.67

0.73

Question

Lazar drives to work every day and passes two independently operated traffic lights. The probability that both lights are green is 0.41. The probability that the first light is green is 0.59. What is the probability that the second light is green, given that the first light is green?

 0.71

 0.69

 0.67

 0.73

anonymous · Answer

@phi

anonymous · Answer

@Callisto

phi · Answer

Use 
$$ Pr(A | B) = \frac{Pr(A \cap B)}{Pr(B)} $$

anonymous · Answer

Okay great!! Can you help me with the plugging in? This is new to me and this formula is strange

anonymous · Answer

Like, what exactly should I plug in for Pr??

anonymous · Answer

Or is that what Im solving for

phi · Answer

the formula says:
Probability of event A given that even B occurred is the probability that both occur divided by the probability that event B occurred.

In your problem, I would let event B be the "first light is green"
and event A be "the 2nd light is green"

anonymous · Answer

Oh dear. So Im gunna give this a shot, correct me if im wrong...

anonymous · Answer

Hey I think i got it. I divided 41 by 59 and got 69. Either it was way simpler than i thought or I did something wrong

phi · Answer

yes, that is the answer. The hard part is understanding why the formula works. Khan has a video if you have time http://www.khanacademy.org/math/trigonometry/prob_comb/prob_combinatorics_precalc/v/conditional-probability-and-combinations

anonymous · Answer

Awesome!! Thanks so much