# Thread: Indepedant events.

1. ## Independant events.

I hope this isn't too long winded, I have most the answers, just need a check and some help on the last part.

Laser surgery to fix short-sightedness is becoming more popular. However, for some people, a second procedure is necessary. The following table lists the joint probability of needing a second procedure and whether the patient has a corrective lens with a factor (dioptre) of minus 8 or less.

This is supposed to be a table!

__________________ Vision corrective factor > -8, Vision corrective factor <= -8

1st procedure successful $\displaystyle ~~~~~~$___________0.66 $\displaystyle ~~~~~~$___________________0.15

2nd procedure required $\displaystyle ~~~~~~$____________0.05 $\displaystyle ~~~~~~$___________________0.14

a) Find the probability that a second procedure is required.

This is simply $\displaystyle 0.05+0.14 = 0.19$

b) Determine the probability that someone whose corrective lens factor is minus 8 or less does not require a second procedure.

This is $\displaystyle 0.66+0.15+0.14 = 0.95$

c) Are the events independent? Explain your answer.

I think the answer is yes, but I don't know how to explain

2. Originally Posted by Bushy
I hope this isn't too long winded, I have most the answers, just need a check and some help on the last part.

Laser surgery to fix short-sightedness is becoming more popular. However, for some people, a second procedure is necessary. The following table lists the joint probability of needing a second procedure and whether the patient has a corrective lens with a factor (dioptre) of minus 8 or less.

This is supposed to be a table!

__________________ Vision corrective factor > -8, Vision corrective factor <= -8

1st procedure successful $\displaystyle ~~~~~~$___________0.66 $\displaystyle ~~~~~~$___________________0.15

2nd procedure required $\displaystyle ~~~~~~$____________0.05 $\displaystyle ~~~~~~$___________________0.14

a) Find the probability that a second procedure is required.

This is simply $\displaystyle 0.05+0.14 = 0.19$

b) Determine the probability that someone whose corrective lens factor is minus 8 or less does not require a second procedure.

This is $\displaystyle 0.66+0.15+0.14 = 0.95$

c) Are the events independent? Explain your answer.

I think the answer is yes, but I don't know how to explain
(b) Pr(2nd procedure NOT required | corrective lens factor < -8) = 0.15/(0.15 + 0.14).

(c) Does Pr(2nd procedure NOT required | corrective lens factor < -8) = Pr(2nd procedure NOT required) ....?